Combination of Mesh Adaptivity with Fluid-Structure ...publications.jrc.ec.europa.eu/repository/bitstream/JRC89728/lbna26617enn.pdfMartin Larcher Alberto Beccantini Combination of

2 0 1 4

Folco Casadei George Valsamos Martin Larcher Alberto Beccantini

Combination of Mesh Adaptivity with

Fluid-Structure Interaction

in EUROPLEXUS

Report EUR 26617 EN

European Commission

Joint Research Centre

Institute for the Protection and Security of the Citizen

Contact information

Martin Larcher

Address: Joint Research Centre, Via Enrico Fermi 2749, TP 480, 21027 Ispra (VA), Italy

E-mail: [email protected]

Tel.: +39 0332 78 9563

Fax: +39 0332 78 9049

http://ipsc.jrc.ec.europa.eu/

http://www.jrc.ec.europa.eu/

This publication is a Technical Report by the Joint Research Centre of the European Commission.

Legal Notice

This publication is a Technical Report by the Joint Research Centre, the European Commission’s in-house science service.

It aims to provide evidence-based scientific support to the European policy-making process. The scientific output expressed

does not imply a policy position of the European Commission. Neither the European Commission nor any person

acting on behalf of the Commission is responsible for the use which might be made of this publication.

JRC89728

ISBN 978-92-79-37851-5

ISSN 1831-9424

DOI 10.2788/61547

Luxembourg: Publications Office of the European Union, 2014

© European Union, 2014

Reproduction is authorised provided the source is acknowledged.

Printed in Italy

i

Contents1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Formulation and implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Syntax of FSI directives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Considerations on the maximum adaptive refinement level . . . . . . . . . . . . . . . . 3

2.3 Adapting the fluid mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3.1 Mesh refinement loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3.2 Mesh unrefinement loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.3 About the ADAP RCON option . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3.4 Optional scaling of the refined zone . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Numerical examples with FE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1 Flying plate in 2D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1.1 Solutions without mesh adaptivity . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1.2 Solutions with mesh adaptivity . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 Flying plate in 3D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22



3.3 Rotating mill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30



4 Numerical examples with CCFV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.1 Flying plate in 2D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39



4.2 Flying plate in 3D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52



5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

List of Figures

1 - Structure influence domain for tightness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 - Progressive scaling of structural influence domain to pilot fluid mesh adaptation . . . . . . . . 6

3 - Definition and initial mesh of the flying plate problem . . . . . . . . . . . . . . . . . . . . . 10

4 - Some results for test FSIA11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14




8 - Comparison of results for tests FSIA11, FSIA12, FSIA13 and FSIA14 . . . . . . . . . . . . 15


10 - Some results for test FSIA09. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

11 - Comparison of results for tests FSIA11, FSIA12, FSIA13, FSIA14, FSIA06 and FSI09 . . . 18

12 - Comparison of results for tests FSIA14 and FSIA09 . . . . . . . . . . . . . . . . . . . . . 19



15 - Definition and initial mesh of the flying plate problem in 3D . . . . . . . . . . . . . . . . . 22




19 - Comparison of results for tests FSIA31, FSIA32 and FSIA33 . . . . . . . . . . . . . . . . 26


21 - Comparison of results for tests FSIA31, FSIA32, FSIA33 and FSIA26. . . . . . . . . . . . 28


23 - Definition of the mill problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

24 - Some results for test MILL11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33




28 - Comparison of results for tests MILL11, MILL12, MILL13 and MILL14 . . . . . . . . . . 34


30 - Comparison of results for tests MILL11, MILL12, MILL13, MILL14 and MILL02 . . . . . 36


32 - Comparison of results for tests MILL14 and MILL04. . . . . . . . . . . . . . . . . . . . . 38


ii







40 - Comparison of results for tests FSIA21, FSIA22, FSIA23, FSIA24, FSIA16 and FSI19 . . . 47








48 - Comparison of results for tests FSIA41, FSIA42 and FSIA43 . . . . . . . . . . . . . . . . 55




iii

iv

List of Tables

1 - Calculations for the FSIA problem with FE in the fluid domain . . . . . . . . . . . . . . . . 10

2 - Calculations for the FSIA problem in 3D with FE in the fluid domain . . . . . . . . . . . . 22

3 - Calculations for the MILL problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4 - Calculations for the FSIA problem with CCFV in the fluid domain . . . . . . . . . . . . . . 39

5 - Calculations for the FSIA problem in 3D with CCFV in the fluid domain. . . . . . . . . . . 52

1. IntroductionThis report is a sequel to reports and publications [1-11] on mesh adaptivity in fast transient dynam-

ics and presents the formulation and implementation of mesh adaptivity in combination with Fluid-

Structure Interaction (FSI) algorithms in fast transient dynamics. The algorithms are implemented in

the EUROPLEXUS code.

EUROPLEXUS [17] is a computer code for fast explicit transient dynamic analysis of fluid-structure

systems jointly developed by the French Commissariat à l’Energie Atomique et aux Energies Alter-

natives (CEA Saclay) and by the Joint Research Centre of the European Commission (JRC Ispra).

Reference [1] presented the first implementation in EUROPLEXUS of an adaptive mesh refinement

and un-refinement procedure, in two space dimensions (element shape QUA4) for solid mechanics.

The procedure was extended to fluid mechanics (FE formulation) in 2D in reference [2]. Then, refer-

ence [3] applied a similar refinement and un-refinement procedure in three space dimensions to the

CUB8 element shape, both in solids mechanics and in fluid mechanics (FE formulation).

All numerical examples presented in references [1-3] with a variable mesh used a so-called “man-

ual” mesh adaptation directive, the WAVE directive (see the code manual in reference [17]), first

introduced in reference [1]. This directive refines the mesh along “wavefronts” that are specified by

the user, e.g. according to a known analytical solution to the problem considered. This technique was

used with success to simulate a bar problem (in solid mechanics) and a shock tube problem (in fluid

mechanics) both in 2D and in 3D [1-3].

However, those solutions cannot be qualified as “true” adaptive solutions, because in (true) adaptiv-

ity mesh refinement and un-refinement should be completely automatic, based upon suitable error

estimators or error indicators. The formulation of error estimators in fast transient dynamics is chal-

lenging and is still a subject of research. The use of so-called error indicators, however, is much sim-

pler. For this reason, subsequent work in EUROPLEXUS focused on error indicators. References [4]

and [5] document a first prototype implementation of adaptivity based upon error indicators in

EUROPLEXUS, limited to 2D problems in continuum and fluid mechanics. An extension of the

indicator technique to 3D is under development but has not been completed and documented yet.

Publications [6-7] focus on the natural quantities of interest in goal-oriented error assessment and

adaptivity, but limited to the case of linear elasto-dynamics.

The adaptive technique was then applied to Cell-Centred Finite Volumes (CCFV) for the description

of the fluid domain, first in 2D (see [8]) and then also in 3D [9]. More recently, the technique has

also been extended for use with the CDEM combustion model which makes use of the CCFV formu-

1

lation [10]. A complete description of the element refinement and un-refinement techniques used in

mesh adaptation has been published in a paper [11].

The present work concerns another aspect of mesh adaptivity, i.e. the automatic refinement of the

fluid mesh near a structure, in order to enhance the treatment of Fluid-Structure Interaction (FSI).

This technique is particularly useful in conjunction with FSI algorithms of the embedded or

immersed type, such as the FLSR or FLSW algorithms available in EUROPLEXUS.

With these algorithms, the interacting fluid and structure are discretized in a completely independent

way at the topological level. Typically, the fluid is represented by a uniform and regular (even struc-

tured) mesh fixed in space (Eulerian description) used as a “background” mesh. The structure is

meshed independently and then it is “embedded” or “immersed” in the fluid mesh. The two meshes

are therefore simply superposed.

A description of the FLSR and FLSW algorithms can be found in references [12-16].

Clearly, the precision of Fluid-Structure coupling depends very much on the use of a sufficiently fine

fluid mesh, at least in the vicinity of the structure, and this is precisely the scope of adaptivity: to

refine the fluid mesh only where it is needed, in this case close to the structure.

This document is organized as follows:

• Section 2 presents the formulation of FSI in conjunction with adaptivity, in particular the strategy

for refining and unrefining the fluid mesh in the vicinity of the structure.

• Section 3 presents some numerical examples for the verification of the proposed algorithms, by

using a FE discretization of the fluid domain.

• Section 4 presents the same examples but by using a CCFV discretization of the fluid domain.

• Some conclusions are given in Section 5.

The Appendix contains a listing of all the input files mentioned in the present report.

2

2. Formulation and implementationIn adaptive calculations with FSI, mesh refinement and un-refinement must occur also in the vicinity

of a structure, in addition to the wavefronts which are tracked via WAVE or INDI directives.

Since this type of mesh adaptation is independent from WAVE or INDI directives, but is related to

the chosen FSI model, it seems preferable to embed the corresponding input directive within the FSI

directives (e.g. FLSR or FLSW).

In principle, the constraints on mesh size resulting from FSI should have to be merged with any con-

straints due to WAVE, INDI or any other (not yet developed) adaptivity directives. The minimum

local mesh size resulting from all such constraints would then have to be retained. However, at the

moment the implementation of WAVE and INDI are such that these models may not be combined in

the same calculation. For simplicity, also the present adaptive FSI model is initially developed and

tested as an independent model, incompatible with WAVE or INDI.

Once all these models are well tested separately, they will have to be re-implemented in a compatible

way by developing a suitable combination strategy.

2.1 Syntax of FSI directives

The FLSR/FLSW directives have the following syntax:

$ FLSR ; FLSW $STRU /LECTS/

$ FLUI /LECTF/ ; STFL $< $ R r ; GAMM gamm ; PHIS phis $ >< $ HGRI hgri ; NMAX nmax ; DELE dele $ >< DGRI >< VOLU ; FACE >< BFLU bflu > < FSCP fscp >< ADAP LMAX lmax <SCAL scal> >

Note that the VOLU or FACE keywords are only available for FLSW.

The ADAP sub-directive is new and introduces adaptivity-related data for the concerned FSI model.

At the moment, the only parameters that can be given are LMAX, the desired maximum fluid mesh

refinement level near the structure, and SCAL, an optional scaling of the adapted zone (see Section

2.3.4).

2.2 Considerations on the maximum adaptive refinement level

In the FLSR/FLSW models for FSI, the structure is coupled with the fluid entities (usually nodes in

the case of FLSR, cell interfaces in the case of FLSW) which are found to be currently located within

the structural influence domain. This domain is formed by circles and quadrilaterals in 2D, by

3

spheres, prisms and hexahedra in 3D. The circles or spheres are centered on the structural nodes

while the other geometric shapes are built by connecting the circles or spheres.

Thus, the thickness of the influence domain at a structural node is the diameter of the associated cir-

cle or sphere. The domain thickness at a point of the structure not coinciding with a node is interpo-

lated from the nodal values around it.

The user can specify the thickness in three alternative ways: by imposing a uniform sphere radius

via the keyword R, or by imposing a variable sphere radius via the keywords GAMM (which is related

to the local fluid mesh size) or PHIS (which is related to the local structure mesh size). In any case,

a sphere radius is finally associated with each structural node, so that the local thickness of the

influence domain is .

In order to ensure tightness, i.e. to avoid spurious fluid passage across a solid structure, the local

thickness of the structure influence domain (i.e. the sphere diameter ) must be greater than

the diagonal of the local fluid mesh cell, see Figure 1. If the fluid mesh is formed by squares in 2D or

cubes in 3D, of size , then in order to ensure tightness it must be

(1)

where is the space dimension (2 or 3).

This condition ensures (at least in the case of a Finite Element formulation for the fluid) that a con-

tinuous layer of fluid entities is coupled with the structure, even in the worst possible case that the

structure is located exactly in the middle between two fluid entities, and has an oblique direction (not

aligned with the global axes).

R

R

D 2R=

D 2R=

h

D d h>d

Figure 1 - Structure influence domain for tightness

h

Structure node

Coupled fluid node

D 2h=

4

Using a value of much larger than the one given by eq. (1) is not advisable, because too much

fluid would be “attached” to the structure. In each practical situation, the minimum value ensuring

tightness is the best one.

When mesh adaptivity is adopted in the fluid domain, the size of the fluid mesh varies according to

the level of refinement. A binary rule is adopted, whereby the size of each level is half that of the

previous level. By convention, the base (ancestor or unrefined) fluid elements are placed at level 1.

Let us therefore denote the size of the base fluid mesh. At any other level of refinement ,

the size of the fluid mesh will be

(2)

i.e. 1/2, 1/4, 1/8 etc. of the base size.

The practical convention is adopted that the user always specifies the FLSR/FLSW data referred to the

base fluid mesh, also in the case of an adaptive calculation. Then, if adaptive FSI is desired, the ADAP

keyword is added to FLSR/FLSW and the LMAX keyword is used to introduce the desired maximum

refinement level (lmax) of the fluid mesh near the structure. In this way, various levels of refinement

can be tried out by changing only the lmax value.

2.3 Adapting the fluid mesh

To obtain a progressively refined fluid mesh near the (moving) structure, from level 1 (base mesh) to

level (the chosen maximum), we proceed as illustrated in Figure 2 where just one structural

element is considered for simplicity. Each used fluid element (base or descendent element, in adap-

tivity) is uniquely identified by the position of its centroid, i.e. the average position of its nodes.

Then, a hierarchy of structural influence domains, similar to the one used to detect FSI, are

built in order to adapt the mesh. Each influence domain is similar to, but has half the thickness as, the

previous one in the hierarchy.

The first (coarsest) influence domain (for ) coincides exactly with the influence domain that

would be used by FLSR/FLSW in the absence of adaptivity, i.e. it has the thickness declared in

the input data set. For example, if a uniform sphere radius has been specified via the R keyword,

then .

The last (finest) influence domain (for ) has thickness . This last

domain is the one automatically used to detect FSI. Therefore, when ADAP LMAX is specified the

radius actually used for FSI is not , but .

D

h1 L 1>

hL

h1

2L 1–

------------=

Lmax

Lmax

L 1=

D1

R1

D1 2R1=

L Lmax= DLmaxD1= 2

Lmax 1–⁄

R1 RLmaxR1 2

Lmax 1–⁄=

5

In the simple illustrative example of Figure 2 we consider refinement up to level 3, i.e. ADAP LMAX

3. We assume that the user has declared in the input file an influence domain radius (or

slightly larger), with the size, assumed here uniform for simplicity, of the base fluid mesh. We

indicate with the diameter (“thickness”) of the base influence domain. This is

used to find the base fluid elements that need to be refined, as shown in a). These are all the fluid ele-

ments whose centroid falls within the influence domain, and are indicated by a cross. In b) we can

see the fluid mesh refined to level 2. Then a scaled-down structure influence domain of thickness

is used to identify the fluid elements which need to be further refined. In c) we can see

the refined fluid mesh at level 3, which is the final one in this case. In this example the option OPTI

ADAP RCON (see Section 2.3.3) is not activated, for simplicity, so in the resulting mesh there remain

some element size transitions that stay in a ratio greater than two. Finally, the code uses the finest

Figure 2 - Progressive scaling of structural influence domain to pilot fluid mesh adaptation

Structure node

Coupled fluid node

h

D1 2h= D2

D1

2------=

Refine Refine

D3

D1

4------=

Element to be refined

Search forcoupledfluidnodes

a) base influence domain and b) influence domain at level 2

c) influence domain at level 3 d) coupled fluid nodes

elements to be refined and elements to be refined

R 2h 2⁄=

h

D1 2R 2h= =

D2 D1 2⁄=

6

influence domain to locate the fluid entities which have to coupled with the structure,

as shown in d). In this example, these entities are simply the fluid nodes (as is typical with the FLSR

algorithm). In case of FLSW, these could also be the cell interfaces.

The complete refinement and un-refinement procedure is as follows.

Two loops are performed at the beginning of each time step to adapt the fluid mesh. In the first loop,

“coarse” fluid elements which now find themselves “near” the structure are (progressively) refined,

while in the second loop “fine” fluid elements which now find themselves “far” from the structure

are (progressively) unrefined.

Each loop proceeds by examining one level at a time. The refinement loop does this in increasing

level order (from level 1 to level ), while the unrefinement loop does this in decreasing

level order, from level to level 1). Note that elements in level are never examined

directly. In fact, they need no refinement since they are already at the maximum refinement level.

Neither are they (directly) examined during unrefinement, because the unrefinement process is nom-

inally applied to the parent element and not to its children.

2.3.1 Mesh refinement loop

The following refinement criterion is adopted. An active element at level is refined (once) if its

centroid lies inside the structure influence domain of level . Active elements in adaptivity are those

which are currently used but have no children, i.e. they are leaves in the elements tree.

Therefore, starting at level 1, all active elements at level 1 (i.e. all active base elements) whose cen-

troid lies within the basic structure influence domain (of thickness ) are refined. to level 2. Next,

we examine active elements at level 2. If such an element lies in the domain of thickness

, then it is refined to level 3. And so on, until we examine elements in level .

The proposed algorithm is as follows.

Algorithm R (refinement)

1. Set level .

2. Increment level: .

3. Loop over the elements .

4. If element is unused, cycle.

5. If element has a level , cycle.

6. If element is inactive, i.e. if it has children, cycle.

7. If the centroid of element is not contained inside the structural influence domain of level ,

characterized by thickness , cycle. This check is done by a fast search procedure

D3 D1 4⁄=

Lmax 1–

Lmax 1– Lmax

L

L

D1

D2 D1 2⁄= Lmax 1–

L 0=

L L 1+=

i

i

i Li L≠

i

i L

DL D1 2L 1–⁄=

7

considering all the structural sub-domains contained (i.e. whose centroid lies) either within the

same spatial cell as element , or in a direct neighbor cell.

8. Refine element .

9. End loop over the elements.

10.If , GO TO 2.

11.End of refinement.

In order to avoid ping-pong effects, the successive unrefinement algorithm should not undo what the

refinement algorithm has just done.

2.3.2 Mesh unrefinement loop

The following unrefinement criterion is adopted. An inactive element at level is unrefined (once)

if its children are all active (i.e. they have no children of their own) and if its centroid does not lie

inside the structure influence domain of level .

Therefore, starting at level , all inactive elements at this level whose centroid does not lie

within the influence domain ( ) are unrefined once to level , and in doing so they

become active while their children become unused. At this particular level there would be no need to

check that the children are active, since they are at the maximum level . Next, we examine inac-

tive elements at level . If such an element has all active children and lies within the influ-

ence domain ( ), then it is unrefined to level . And so on, until we examine elements

at level 1. The proposed algorithm is as follows.

Algorithm U (unrefinement)

1. Set level .

2. Decrement level: .

3. Loop over the elements .

4. If element is unused, cycle.

5. If element has a level , cycle.

6. If element is active, i.e. if it has no children, cycle.

7. If any of the children of element is inactive, i.e. if it has its own children, cycle.

8. If the centroid of element is contained inside the structural influence domain of level , charac-

terized by thickness , cycle. This check is done by a fast search procedure con-

sidering all the structural sub-domains contained (i.e. whose centroid lies) either within the same

spatial cell as element , or in a direct neighbor cell.

i

i

L Lmax

1–<

L

L

Lmax 1–

DLmax 1– Lmax 2–

Lmax

Lmax 2–

DLmax 2– Lmax 3–

L Lmax=

L L 1–=

i

i

i Li L≠

i

i

i L

DL D1 2L 1–⁄=

i

8

9. Unrefine element .

10.End loop over the elements.

11.If , GO TO 2.

12.End of refinement.

2.3.3 About the ADAP RCON option

Note that in order to ensure correct functioning of the refinement and unrefinement loops, elements

should be refined or unrefined just by one level at a time and this must in principle have no effect on

the neighboring elements. In other words, the option ADAP RCON should in principle be disabled for

prudence.

This option is sometimes used with the other adaptivity algorithms (WAVE or INDI) in order to ensure

smooth mesh transition. In the case of adaptive FSI, however, the mesh transition is completely con-

trolled by the refinement and unrefinement algorithms described above. The use of ADAP RCON is

therefore, at least in principle, incompatible with adaptive FSI and could possibly lead to ping-pong

effects (i.e. immediate un-refinement of elements which have been just refined at the same step of

the time loop), and thus to bad results.

However, preliminary tests by adding a check of ping-pong operations (which has a certain cost,

however) seem to indicate that in practice, at least in the first tests performed, no ping-pong occurs.

Therefore, the code does not stop if the ADAP RCON option is used in conjunction with FSI.

2.3.4 Optional scaling of the refined zone

In alternative (or in addition) to the ADAP RCON option described in the previous Section, users may

want to impose a scaling factor to the refined zone. This can be done by specifying ADAP LMAX

lmax SCAL scal in the FLSR or FLSW input directives. By default, .

The scaling factor applies to all influence domains used for the mesh adaptivity process, from level

1 to level . However, the factor does not apply to the search of the fluid entities in interaction

with the structure.

For example, by specifying one would obtain a twice thicker refined fluid mesh zone around

the structure, at each level of refinement. This is likely to produce a smooth mesh size transition even

without specifying the ADAP RCON option. However, changing has no influence on the thickness

used to detect the fluid entities (nodes or interfaces) and thus the number of interacting fluid nodes or

interfaces does not depend upon .

i

L 1>

s

s 1=

s

Lmax

s 2=

s

s

9

3. Numerical examples with FEWe present some numerical examples in order to test the algorithms described in the previous Sec-

tion. We start by considering FE discretizations of the fluid domain. In the next Section the same

tests will then be repeated by using CCFV discretizations of the fluid domain.

3.1 Flying plate in 2D

The first example is that of a metallic plate flying at a certain initial velocity within a square domain

containing a compressible fluid, see Figure 3. The fluid domain (perfect gas material) has a dimen-

sion of m and its walls are rigid (but the fluid can slide along the walls without any resis-

tance). The plate, made of steel-like elasto-plastic material, is located at 1.5 units from the left wall

of the fluid domain, has a length of 7 m and an initial velocity of 100 m/s. In all cases, the plate is

modelled by just 7 shell elements of type ED01.

First, a reference solution is obtained by means of non-adaptive calculations with more and more

refined fluid meshes. Then, adaptive calculations are tested. All performed calculations are summa-

rized in Table 1.

Case Fluid Mesh Notes Steps CPU [s] Els*step

FSIA11 100 FL24 No adaptivity 961 0.7 102,934

FSIA12 400 FL24 No adaptivity 961 1.0 391,534

FSIA13 1,600 FL24 No adaptivity 961 2.8 1,545,934

FSIA14 6,400 FL24 No adaptivity 1,180 12.4 7,566,667

FSIA06 base: 100 FL24 ADAP LMAX 3, RCON 961 1.7 223,156

FSIA09 base: 100 FL24 ADAP LMAX 4, RCON 1,123 2.8 457,906

Table 1 - Calculations for the FSIA problem with FE in the fluid domain

10 10×

Figure 3 - Definition and initial mesh of the flying plate problem

v0 100=

Base fluid mesh

Structure

10

3.1.1 Solutions without mesh adaptivity

FSIA11

This test uses a very coarse fluid mesh, of just FL24 quadrilateral fluid elements. The initial

FLSR structural domains and coupled fluid nodes are shown in the first part of Figure 4. Then are

shown the same quantities, the pressure field and the velocity field at 50 ms (half of the transient cal-

culation) when the fluid flow is already well-developed.

FSIA12

This test is similar to the previous one but uses a more refined fluid mesh, of FL24 quadri-

laterals. Some results of this test are shown in Figure 5.

FSIA13



FSIA14



Figure 8 compares results of all four calculations, showing the displacement and velocity of a node

near the center of the plate. It can be seen that, apart the coarsest-mesh case (FSIA11), the solution is

only slightly sensitive to fluid mesh fineness, if one considers only the plate motion. We will assume

as reference the solution with the finest mesh (FSIA14), i.e. the green curves in Figure 8.

3.1.2 Solutions with mesh adaptivity

FSIA06

This test uses a base fluid mesh of FL24 quadrilateral fluid elements, exactly like in case

FSIA11. However, in the FLSR directive we specify ADAP LMAX 3, i.e. adaptive refinement near the

structure up to a level 3 (thus a refinement of up to a factor 4 with respect to the base mesh), which

would correspond to a fluid mesh of the same size locally as case FSIA13. Some results of this test

are shown in Figure 9.

In this case use has been made of the OPTI ADAP RCON option in order to keep the adapted mesh

always graded. Without this option, the jump in mesh size between two neighboring fluid elements

FSIA10 base: 100 FL24 ADAP LMAX 4 SCAL 2 1,132 3.3 650,677


Table 1 - Calculations for the FSIA problem with FE in the fluid domain

10 10×

20 20×

40 40×

80 80×

10 10×

11

was more than 2, in some cases. Despite use of the option, no ping-pong effects were detected by the

dedicated check.

The solution is similar to the one of case FSIA13, although the base mesh is the one with only

elements, which is too coarse (since in the preliminary study the solution with this mesh

was quite bad). Probably, a better choice would be that of using at least a base mesh (like in

case FSIA12). This would substantially improve the result in the non-refined zones of the mesh with

only a very marginal increase of the CPU time.

Note that in this calculation the user specifies the FLSR directive exactly like in the case without

adaptivity (apart from the additional ADAP LMAX keyword). In other words, we use an FLSR radius

(for a square base mesh of size 1.0), the same as in case FSIA11, while in the case

FSIA13 (without adaptivity) we had to specify , i.e of the previous value.

FSIA09

This test is similar to FSIA06 but in the FLSR directive we specify ADAP LMAX 4, i.e. adaptive

refinement near the structure up to a level 4 (thus a refinement of up to a factor 8 with respect to the

base mesh), which would correspond to a fluid mesh of the same size as case FSIA14. Some results

of this test are shown in Figure 10.

Again, we specify an FLSR radius (for a square base mesh of size 1.0), the same as in

case FSIA11, because this is the value related to the base fluid mesh.

This solution is very similar to FSIA06, the main difference being due to the better resolution in the

zones above and below the plate (which are meshed too coarsely in the first case). It should be noted

that the CPU time required for a level-4 locally adaptive calculation is less than twice the one needed

for the corresponding level-3 calculation. With the same two mesh sizes, not only are the non-adap-

tive calculations more expensive in absolute terms, but the ratio of CPU times in that case is more

than 4.

In other words, uniform-mesh calculations rapidly become impossible due to excessive CPU time as

the mesh size is reduced, while locally adaptive ones remain affordable even at very fine local mesh

(which is needed to have good accuracy of the FSI algorithm).

A comparison of all 6 calculations (4 without and 2 with adaptivity) is given in Figure 11 in terms of

plate displacement and velocity. The finest-mesh solutions FSIA14 and FSIA09 are very similar.

They are compared alone in Figure 12 for clarity.

10 10×

20 20×

R 0.7072=

R 0.1768= 1 4⁄

R 0.7072=

12

FSIA10

This test is similar to FSIA09 but does not use the OPTI ADAP RCON option and a SCAL 2.0

optional parameter in the FLSR directive instead.

Some results for this test are presented in Figure 13. Note how the adapted fluid mesh remains natu-

rally graded despite the lack of the ADAP RCON option. The number of elements and nodes to be

allocated in the adaptive process is larger than in case FSIA09, but this is normal since the refined

zone is larger. However, the number of fluid nodes interacting with the structure, and thus the mass

of fluid “attached” to the structure, is exactly the same in the two cases. This solution is very similar

to FSIA09.

The finest-mesh solutions FSIA14 and FSIA10 are very similar. They are compared in Figure 14.

13

Figure 4 - Some results for test FSIA11




14

Figure 8 - Comparison of results for tests FSIA11, FSIA12, FSIA13 and FSIA14

15


16


17

Figure 11 - Comparison of results for tests FSIA11, FSIA12, FSIA13, FSIA14, FSIA06 and FSI09

18

Figure 12 - Comparison of results for tests FSIA14 and FSIA09

19


20


21


The next example is the 3D version of the flying plate shown in the previous Section, see Figure 15.

The plate is square in shape with side 7 m and is located at m. It is modelled by 49 shell ele-

ments of type Q4GS.



rized in Table 2.


FSIA31

This test uses a very coarse fluid mesh, of just FL38 hexahedral fluid elements. The

initial FLSR structural domains and coupled fluid nodes are shown in the first part of Figure 16.

Then are shown the same quantities, the pressure field and the velocity field at 50 ms (half of the

transient calculation) when the fluid flow is already well-developed.





FSIA26 base: 1000 FL38 ADAP LMAX 3, RCON 966 919.2 5,172,782

Table 2 - Calculations for the FSIA problem in 3D with FE in the fluid domain

x 1.5=

Figure 15 - Definition and initial mesh of the flying plate problem in 3D

v0 100=

Fluid mesh

Plate mesh

10 10× 10×

22

FSIA32

This test is similar to the previous one but uses a more refined fluid mesh, of FL38

hexahedra. Some results of this test are shown in Figure 17.

FSIA33

This test is similar to the previous one but uses a more refined fluid mesh, of FL38


Figure 19 compares results of all three calculations, showing the displacement and velocity of a node


only slightly sensitive to fluid mesh fineness, if one considers only the plate motion. We will assume

as reference the solution with the finest mesh (FSIA33), i.e. the cyan curves in Figure 19.


FSIA26

This test uses a base fluid mesh of FL38 hexahedra fluid elements, exactly like in case

FSIA31. However, in the FLSR directive we specify ADAP LMAX 3, i.e. adaptive refinement near the

structure up to a level 3 (thus a refinement of up to a factor 4 with respect to the base mesh), which

would correspond to a fluid mesh of the same size locally as case FSIA33. Some results of this test

are shown in Figure 20. In this case use has been made of the OPTI ADAP RCON option without any

ping-pong effects being detected by the dedicated check.

The solution is reasonably similar to the one of case FSIA33.




As it results from Table 2, the cost of the adaptive calculation FSIA26 is 2.15 times higher than that

of the correspondingly fine calculation without adaptivity, which is very disappointing. However,

there is an explanation for this. In the case of FLSR, the coupling between fluid an structure is done

in a strong manner, i.e. by means of Lagrange multipliers, or kinematic links. In addition to these

links, some other links are also required at the so-called hanging nodes generated in the adaptive

mesh refinement. From the listings of the calculations, one can see that already in case FSIA33 the

code spends 53% of the CPU time in solving the links, and only 43% in computing the elements.

This is due to several reasons:

• First of all, the standard Choleski solver is employed, which can be relatively inefficient on large

systems.

20 20× 20×

40 40× 40×

10 10× 10×

23

• Second, in case of strong coupling between a relatively coarse structure and a (much) finer fluid

mesh, the bandwidth of the system is known to increase, so that the system solution takes more

time.

• Third, by default the code splits the links in several independent sub-systems. This operation may

be inefficient in some cases and can increase substantially the CPU time.

In the adaptive calculation FSIA26, in addition to the FLSR links we have also the adaptivity-related

links at hanging nodes (this is so because we are using FE for the fluid domain in this solution). The

result is that the code spends as much as 97% of CPU time in solving the links, and only 2% in com-

puting the elements. The result is that this calculation costs more than the non-adaptive one.

To ameliorate the situation, one may try the following:

• Use a more efficient system solver, such as SPLIB. (SOLV SPLI).

• Refine the structure mesh. Although this will augment the number of structure elements and

reduce the associated time step, the bandwidth of the links system will decrease. Sometimes the

global effect of all these parameters is a reduction of the CPU time (rather than an increase as it

would seem logical).

• Avoid splitting the links system (SPLT NONE). The solution of a monolithic system is sometimes

faster than splitting and then solving several independent subsystems, since the solver is quite

efficient.

Note that in theory all these drawbacks are avoided if one uses a weak, rather than a strong, F-S cou-

pling. To this end, one might try out the decoupled (weak) version of FLSR (activated by directive

LINK DECO FLSR instead of LINK COUP FLSR), which could work provided there is no physical

interaction between the FSI constraints and other constraints (such as blockages on the fluid enve-

lope or constraints at hanging nodes).

Even better, one could avoid all these drawbacks by using the CCFV formulation for the fluid

domain, and the associated weak coupling LINK DECO FLSW. A further advantage, in this case,

would be that no links are needed on the fluid envelope, and also no links are needed at hanging

nodes, because the velocities are at the cell centres and not at nodes in this case. Thus, an adaptive

calculation with CCFV would require no links at all. Such a calculation is presented in Section 4.2.

24




25

Figure 19 - Comparison of results for tests FSIA31, FSIA32 and FSIA33

26


27


28


29

3.3 Rotating mill

The second example is that of a metallic mill rotating at a certain initial velocity within a square

domain containing a compressible fluid, see Figure 23. The fluid domain (perfect gas material) has a

dimension of m and its walls are rigid (but the fluid can slide along the walls without any

resistance). The mill, made of steel-like elasto-plastic material, is located at the centre of the fluid

domain, has two blades of length 8 m each and an initial velocity of 80 m/s at the blade tips (linear

initial velocity distribution along the blades). In all cases, the mill is modelled by just 16 shell ele-

ments of type ED01 (8 elements in each blade).

First, a reference solutions is obtained by means of non-adaptive calculations with more and more


rized in Table 3.


MILL11 100 FL24 No adaptivity 961 0.8 111,592

MILL12 400 FL24 No adaptivity 961 1.3 400,192

MILL13 1,600 FL24 No adaptivity 961 3.4 1,554,592

MILL14 6,400 FL24 No adaptivity 962 12.2 6,178,608

MILL02 base: 100 FL24 ADAP LMAX 4, RCON 1,002 7.1 751,064

MILL04 base: 100 FL24 ADAP LMAX 4 SCAL 2 1,002 6.8 1,063,776

Table 3 - Calculations for the MILL problem

10 10×

Figure 23 - Definition of the mill problem

v0 80=

30


MILL11

This test uses a very coarse fluid mesh, of just FL24 quadrilateral fluid elements. The initial

FLSR structural domains and coupled fluid nodes are shown in the first part of Figure 24. Then are

shown the same quantities, the pressure field and the velocity field at 100 ms (end of the transient

calculation) when the mill has rotated clockwise by about 100 degrees.

MILL12



MILL13



MILL14




at the tip of one of the blades. It can be seen that the solution is only slightly sensitive to fluid mesh

fineness, if one considers only the blades motion. We will assume as reference the solution with the

finest mesh (MILL14), i.e. the green curves in Figure 28.


MILL02

This test uses a base fluid mesh of FL24 quadrilateral fluid elements, exactly like in case

MILL11. However, in the FLSR directive we specify ADAP LMAX 4, i.e. adaptive refinement near

the structure up to a level 4 (thus a refinement of up to a factor 8 with respect to the base mesh),

which would correspond to a fluid mesh of the same size as case MILL14. Some results of this test





dedicated check.

10 10×

20 20×

40 40×

80 80×

10 10×

31

The solution is very different from those without adaptivity. The blades bend much more from the

very beginning and plastify. Also, some parasitic high velocities are observed near the blades at the

beginning of the transient. This solution is therefore considered unacceptable.

The difference in solutions can be better appreciated in Figure 30.

MILL04

This test is identical to MILL02 but uses SCAL 2.0 instead of OPTI ADAP RCON in order to widen

the refined zone and to keep the adapted mesh smoothly graded.

The solution now is free from parasitic velocities, and very similar to the one obtained without adap-

tivity and a fine mesh, case MILL14. Some results of this test are shown in Figure 31. The adapted

fluid mesh remains smoothly graded during the entire transient computation.

The solution in terms of blade displacement and velocity is compared with the finest uniform-mesh

solution (MILL14) in Figure 32, showing almost perfect agreement.

32

Figure 24 - Some results for test MILL11




33

Figure 28 - Comparison of results for tests MILL11, MILL12, MILL13 and MILL14

34


35

Figure 30 - Comparison of results for tests MILL11, MILL12, MILL13, MILL14 and MILL02

36


37

Figure 32 - Comparison of results for tests MILL14 and MILL04

38

4. Numerical examples with CCFVWe consider now the same numerical examples as in the previous Section, but by using a CCFV dis-

cretization of the fluid sub-domain instead of a FE discretization. The FLSW coupling directive is

therefore used and tested, instead of FLSR.


The problem has been already defined in Section 3.1, see Figure 3. Here the same calculations are

repeated by using the CCFV element Q4VF instead of FL24, and the LINK DECO FLSW coupling

directive instead of LINK COUP FLSR. The parameter FACE is added to the FLSW directive. This

optional keyword is only available with FLSW (not with FLSR) and searches directly for the coupled

CCFV interfaces, rather than for the coupled volume centroids.

No options are specified for the CCFV, so the default options are taken: second-order without recon-

struction (i.e. first-order) solution, HLLC flux solver, etc.



rized in Table 4.


FSIA21

This test uses a very coarse fluid mesh, of just Q4VF quadrilateral fluid elements. The ini-

tial FLSW structural domains and coupled fluid nodes are shown in the first part of Figure 33. Then

are shown the same quantities, the pressure field and the velocity field at 50 ms (half of the transient

calculation) when the fluid flow is already well-developed.


FSIA21 100 Q4VF No adaptivity 961 0.6 102,934

FSIA22 400 Q4VF No adaptivity 961 1.1 391,534

FSIA23 1,600 Q4VF No adaptivity 961 3.7 1,545,934

FSIA24 6,400 Q4VF No adaptivity 1,026 17.2 6,579,989

FSIA16 base: 100 Q4VF ADAP LMAX 3, RCON 961 1.3 220,075

FSIA19 base: 100 Q4VF ADAP LMAX 4, RCON 961 2.1 394,000

FSIA20 base: 100 Q4VF ADAP LMAX 4 SCAL 2 961 3.1 554,482

Table 4 - Calculations for the FSIA problem with CCFV in the fluid domain

10 10×

39

FSIA22

This test is similar to the previous one but uses a more refined fluid mesh, of Q4VF quadri-


FSIA23



FSIA24





only slightly sensitive to fluid mesh fineness, if one considers only the plate motion. However, we

will assume as reference the solution with the finest mesh (FSIA24), i.e. the green curves in Figure

37.


FSIA16

This test uses a base fluid mesh of Q4VF quadrilateral fluid elements, exactly like in case

FSIA21. However, in the FLSW directive we specify ADAP LMAX 3, i.e. adaptive refinement near

the structure up to a level 3 (thus a refinement of up to a factor 4 with respect to the base mesh),

which would correspond to a fluid mesh of the same size as case FSIA23. Some results of this test





dedicated check.

The solution is similar to the one of case FSIA23, although the base mesh is the one with only

elements, which is too coarse (since in the preliminary study the solution with this mesh

was quite bad). Probably, a better choice would be that of using at least a base mesh (like in

case FSIA12). This would substantially improve the result in the non-refined zones of the mesh with

only a very marginal increase of CPU time.

Note that in this calculation the user specifies the FLSW directive exactly like in the case without

adaptivity (apart from the additional ADAP LMAX keyword). In other words, we use an FLSW radius

20 20×

40 40×

80 80×

10 10×

10 10×

20 20×

40

(for a square base mesh of size 1.0), the same as in case FSIA21, while in the case

FSIA23 (without adaptivity) we had to specify , i.e of the previous value.

FSIA19

This test is similar to FSIA16 but in the FLSW directive we specify ADAP LMAX 4, i.e. adaptive

refinement near the structure up to a level 4 (thus a refinement of up to a factor 8 with respect to the

base mesh), which would correspond to a fluid mesh of the same size as case FSIA24. Some results

of this test are shown in Figure 39.

Again, we specify an FLSW radius (for a square base mesh of size 1.0), the same as in

case FSIA21, because this is the value related to the base fluid mesh.

This solution is very similar to FSIA16, the main difference being due to the better resolution in the

zones above and below the plate (which are meshed too coarsely in the first case). It should be noted

that the CPU time required for a level-4 locally adaptive calculation is less than twice the one needed

for the corresponding level-3 calculation. With the same two mesh sizes, not only are the non-adap-

tive calculations more expensive in absolute terms, but the ratio of CPU times in that case is more

than 4.

In other words, uniform-mesh calculations rapidly become impossible due to excessive CPU time as

the mesh size is reduced, while locally adaptive ones remain affordable even at very fine local mesh

(which is needed to have good accuracy of the FSI algorithm).




Finally, Figure 42 compares the solutions FSIA14 and FSIA24, i.e. the non-adaptive and adaptive

solutions with the finest meshes.

FSIA20

This test is similar to FSIA19 but does not use the OPTI ADAP RCON option and a SCAL 2.0

optional parameter in the FLSW directive instead.

Some results for this test are presented in Figure 43. Note how the adapted fluid mesh remains natu-

rally graded despite the lack of the ADAP RCON option. The number of elements and nodes to be

allocated in the adaptive process is larger than in case FSIA19, but this is normal since the refined

zone is larger. However, the number of fluid interfaces interacting with the structure, and thus the

mass of fluid “attached” to the structure, is exactly the same in the two cases. This solution is similar

to FSIA19.

R 0.7072=

R 0.1768= 1 4⁄

R 0.7072=

41

The finest-mesh solutions FSIA14 and FSIA20 are reasonably similar. They are compared in Figure

44.

42





43


44


45


46

Figure 40 - Comparison of results for tests FSIA21, FSIA22, FSIA23, FSIA24, FSIA16 and FSI19

47


48


49


50


51


The problem has been already defined in Section 3.2, see Figure 15. Here the same calculations are

repeated by using the CCFV element CUVF instead of FL38, and the LINK DECO FLSW coupling

directive instead of LINK COUP FLSR. The parameter FACE is added to the FLSW directive. This

optional keyword is only available with FLSW (not with FLSR) and searches directly for the coupled

CCFV interfaces, rather than for the coupled volume centroids.

No options are specified for the CCFV, so the default options are taken: second-order without recon-

struction (i.e. first-order) solution, HLLC flux solver, etc.



rized in Table 5.


FSIA41

This test uses a very coarse fluid mesh, of just CUVF hexahedral fluid elements. The

initial FLSW structural domains and coupled fluid nodes are shown in the first part of Figure 45.

Then are shown the same quantities, the pressure field and the velocity field at 50 ms (half of the

transient calculation) when the fluid flow is already well-developed.

FSIA42

This test is similar to the previous one but uses a more refined fluid mesh, of CUVF


FSIA43

This test is similar to the previous one but uses a more refined fluid mesh, of CUVF


Figure 48 compares results of all three calculations, showing the displacement and velocity of a node

near the center of the plate. It can be seen that in this case the solution converges less clearly than in


FSIA41 1,000 CUVF No adaptivity 963 5.6 1,011,236



FSIA36 base: 1,000 CUVF ADAP LMAX 3 962 78.0 5,175,299

Table 5 - Calculations for the FSIA problem in 3D with CCFV in the fluid domain

10 10× 10×

20 20× 20×

40 40× 40×

52

the similar calculations with FE. Nevertheless, we will assume as reference the solution with the fin-

est mesh (FSIA43), i.e. the cyan curves in Figure 48.


FSIA36

This test uses a base fluid mesh of CUVF hexahedral fluid elements, exactly like in

case FSIA41. However, in the FLSW directive we specify ADAP LMAX 3, i.e. adaptive refinement

near the structure up to a level 3 (thus a refinement of up to a factor 4 with respect to the base mesh),

which would correspond to a fluid mesh of the same size as case FSIA43. Some results of this test


In this case use has been made of the OPTI ADAP RCON option. Despite use of the option, no ping-

pong effects were detected by the dedicated check.

The solution is similar to the one of case FSIA43, but even more to that of case FSIA42, which cor-

responds to a refinement of level 2 instead of 3.


plate displacement and velocity. The finest-mesh solutions FSIA43 and FSIA36 are relatively simi-

lar. They are compared alone in Figure 51 for clarity.

As can be seen from Table 5, with CCFV and FLSW (weak or decoupled links) the speed-up factor

between the calculations without and with adaptivity is 3.1 (greater than 1, unlike in the case with FE

and FLSR).

10 10× 10×

53




54

Figure 48 - Comparison of results for tests FSIA41, FSIA42 and FSIA43

55


56


57


58

5. ConclusionsIn this report the automatic adaptation (refinement, un-refinement) of fluid mesh in the vicinity of a

moving structure has been presented. The adapted fluid mesh interacts with the structure by means of

so-called embedded FSI algorithms, namely the FLSR (strong coupling by means of Lagrange multi-

pliers) and the FLSW (weak coupling by means of direct pressure force transmission) algorithms.

The implementation is done in 2D and 3D and covers Finite Element as well as Cell Centred Finite

Volume discretizations of the fluid domain. The input directives are very simple and various levels of

refinement (LMAX) can be tested by changing a single value in the input file.

The numerical examples show that the technique allows calculations with locally fine fluid mesh

with just a fraction of the memory (number of elements) that would be required with a uniformly

refined fluid mesh.

As concerns CPU times, a gain may or may not be obtained depending on circumstances. When

using the strong version of FSI (i.e. the “coupled” version of the FLSR algorithm, suitable for FE),

the calculation time is sometimes penalized by the large number of constraints and by the solution of

the system to obtain the Lagrange multipliers (the interaction forces). The chosen adaptive scheme

adds constraints at hanging nodes, which must be combined with FSI-related and other constraints.

With the weak version of FSI (i.e. the FLSW algorithm, suitable for CCFV) there are two advan-

tages. First, no constraints are required for the FSI, by definition. But also no constraints are required

at hanging nodes in this case, because the fluid velocities are discretized at cell centres, not at nodes.

Therefore, a calculation of this type can be done without any (coupled) constraints, resulting often in

a larger gain than in the previous case.

A version of FLSR not using Lagrange multipliers (the so-called LINK DECO FLSR model) is also

available in the code. This might be an interesting alternative allowing to obtain larger CPU gains in

combination with FE descriptions of the fluid domain. However, the combination of adaptivity with

this FSI model is not yet complete and will be finalized in a forthcoming report.

59

6. References[1] F. CASADEI, P. DÍEZ, F. VERDUGO: “A Data Structure for Adaptivity in EUROPLEXUS”, JRC

Technical Note PUBSY N. JRC60795, September 2010.

[2] F. CASADEI, P. DÍEZ, F. VERDUGO: “Adaptivity in FE Models for Fluids in EUROPLEXUS”,

JRC Technical Note PUBSY N. JRC61622, November 2010.

[3] F. CASADEI, P. DÍEZ, F. VERDUGO: “Adaptive 3D Refinement and Un-refinement of 8-node

Solid and Fluid Hexahedra in EUROPLEXUS”, JRC Technical Note PUBSY N. JRC63833,

March 2011.

[4] F. CASADEI, P. DÍEZ, F. VERDUGO: “Implementation of a 2D Adaptivity Indicator for Fast Tran-

sient Dynamics in EUROPLEXUS”, JRC Technical Note PUBSY N. JRC64506, April 2011.

[5] F. CASADEI, P. DÍEZ, F. VERDUGO: “Further Development of 2D Adaptivity Error Indicators in

EUROPLEXUS”, JRC Technical Note, PUBSY No. JRC66337, September 2011.

[6] F. VERDUGO, P. DÍEZ, F. CASADEI: “Natural quantities of interest in linear elastodynamics for

goal oriented error estimation and adaptivity”, Proceedings of the V International Conference

on Adaptive Modeling and Simulation (ADMOS 2011), D. Aubry and P. Díez (Eds), Paris,

France, 6-8 June 2011.

[7] F. VERDUGO, P. DÍEZ, F. CASADEI: “General form of the natural quantities of interest for goal

oriented error assessment and adaptivity in linear elastodynamics”, Submitted for publication in

the International Journal for Numerical Methods in Engineering, DOI: 10.1002/nme, PUBSY

No. JRC65788, July 2011.

[8] F. CASADEI, G. VALSAMOS, P. DÍEZ, F. VERDUGO: “Implementation of Adaptivity in 2D Cell

Centred Finite Volumes in EUROPLEXUS”, Technical Note, PUBSY No. JRC67859, Decem-

ber 2011.

[9] F. CASADEI, P. DÍEZ, F. VERDUGO: “Implementation of Adaptivity in 3D Cell Centred Finite

Volumes in EUROPLEXUS”, Technical Note, PUBSY No. JRC68168, December 2011.

[10] F. CASADEI, P. DÍEZ, F. VERDUGO: “Testing Adaptivity in 2D Cell Centred Finite Volumes with

the CDEM Combustion Model in EUROPLEXUS”, Technical Note, PUBSY No. JRC68333,

December 2011.

[11] F. CASADEI, P. DÍEZ, F. VERDUGO: “An algorithm for mesh refinement and un-refinement in

fast transient dynamics”, International Journal of Computational Methods, DOI 10.1142/

S0219876213500187, Vol. 10, No. 4, pp. 1350018-1 / 1350018-31, 2013.

[12] F. CASADEI: “Fast Transient Fluid-Stucture Interaction with Failure and Fragmentation”,

60

Extended abstract submitted for presentation at the 8th World Congress on Computational

Mechanics (WCCM8), Venice, Italy, June 30 - July 5, 2008.

[13] F. CASADEI, N. LECONTE: “Use of FLSR Fluid-Structure Interaction with Node-Centered Finite

Volumes in EUROPLEXUS. Technical Note, PUBSY No. JRC59686, August 2010.

[14] F. CASADEI, N. LECONTE: “FLSW : A Weak, Embedded-Type Fluid-Structure Interaction

Model with CCFV in EUROPLEXUS”, Technical Note, PUBSY No. JRC65826, July 2011.

[15] F. CASADEI, M. LARCHER, N. LECONTE: “Strong and weak forms of a fully non-conforming FSI

algorithm in fast transient dynamics for blast loading of structures”, PUBSY No. JRC60824.

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tural Dynamics and Earthquake Engineering, Corfu, Greece, May 25{28, 2011.

[16] A. BECCANTINI, F. CASADEI, P. GALON: “Improvement of the FLSW model for Cell-Centered

Finite Volumes in EUROPLEXUS. Report DEN/DANS/DM2S/STMF/LATF/NT/13-019/A,

April 2013.

[17] “EUROPLEXUS User’s Manual”, on-line version: http://europlexus.jrc.ec.europa.eu.

61

fsia06.epx 28 February 2014 9:04 am

Appendix

Sample input files

This Section contains, in alphabetical file order, thelistings of all input files related to the exampleswhich were proposed in the previous Sections.

fsia06.epx FSIA06ECHO!CONV winDPLA ALEDIME

ADAP NPOI 205 FL24 232 ENDANALE 1 NBLE 1

TERMGEOM LIBR POIN 129 FL24 100 ED01 7 TERM0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 00 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 10 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 20 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 3 10 30 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 4 10 40 5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 10 50 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 9 6 10 60 7 1 7 2 7 3 7 4 7 5 7 6 7 7 7 8 7 9 7 10 70 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 8 9 8 10 80 9 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 9 10 90 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 101.5 1.5 1.5 2.5 1.5 3.5 1.5 4.51.5 5.5 1.5 6.5 1.5 7.5 1.5 8.51 2 13 12 2 3 14 13 3 4 15 14 4 5 16 15 5 6 17 166 7 18 17 7 8 19 18 8 9 20 19 9 10 21 20 10 11 22 2112 13 24 23 13 14 25 24 14 15 26 25 15 16 27 26 16 17 28 2717 18 29 28 18 19 30 29 19 20 31 30 20 21 32 31 21 22 33 3223 24 35 34 24 25 36 35 25 26 37 36 26 27 38 37 27 28 39 3828 29 40 39 29 30 41 40 30 31 42 41 31 32 43 42 32 33 44 4334 35 46 45 35 36 47 46 36 37 48 47 37 38 49 48 38 39 50 4939 40 51 50 40 41 52 51 41 42 53 52 42 43 54 53 43 44 55 5445 46 57 56 46 47 58 57 47 48 59 58 48 49 60 59 49 50 61 6050 51 62 61 51 52 63 62 52 53 64 63 53 54 65 64 54 55 66 6556 57 68 67 57 58 69 68 58 59 70 69 59 60 71 70 60 61 72 7161 62 73 72 62 63 74 73 63 64 75 74 64 65 76 75 65 66 77 7667 68 79 78 68 69 80 79 69 70 81 80 70 71 82 81 71 72 83 8272 73 84 83 73 74 85 84 74 75 86 85 75 76 87 86 76 77 88 8778 79 90 89 79 80 91 90 80 81 92 91 81 82 93 92 82 83 94 9383 84 95 94 84 85 96 95 85 86 97 96 86 87 98 97 87 88 99 9889 90 101 100 90 91 102 101 91 92 103 102 92 93 104 10393 94 105 104 94 95 106 105 95 96 107 106 96 97 108 10797 98 109 108 98 99 110 109100 101 112 111 101 102 113 112 102 103 114 113 103 104 115 114104 105 116 115 105 106 117 116 106 107 118 117 107 108 119 118108 109 120 119 109 110 121 120122 123 123 124 124 125 125 126 126 127127 128 128 129

COMP GROU 2 'flui' LECT 1 PAS 1 100 TERM'stru' LECT 101 PAS 1 107 TERM

NGRO 2 'blox' LECT 1 PAS 11 111 11 PAS 11 121 TERM'bloy' LECT 1 PAS 1 11 111 PAS 1 121 TERM

COUL turq LECT flui TERMvert LECT stru TERM

EPAI 0.01 LECT stru TERMGRIL LAGR LECT stru TERM

EULE LECT flui TERMMATE FLUT RO 1.0 EINT 2.5E5 GAMM 1.4 PB 0

ITER 1 ALF0 1 BET0 1 KINT 0 AHGF 0 CL 0.5CQ 2.56 PMIN 0 NUM 1 PREF 1.E5LECT flui _fl24 TERM

VM23 RO 7800. YOUNG 1.6E11 NU 0.333 ELAS 1.05E8TRAC 2 1.05E8 .656256E-3 1.6105E10 1.00066LECT stru TERM

LINK COUPBLOQ 1 LECT blox TERMBLOQ 2 LECT bloy TERMFLSR STRU LECT stru TERM

FLUI LECT flui TERMR 0.7072 ! so that d = 2r = 1.4144HGRI 1.6DGRI

!BFLU 0 FSCP 1BFLU 0 FSCP 0ADAP LMAX 3

INIT VITE 1 100.0 LECT stru TERMECRI DEPL VITE ACCE FINT FEXT TFRE 10.E-3

POIN LECT stru TERMELEM LECT stru TERM

FICH ALIC FREQ 1 !TFRE 1.E-3OPTI NOTECSTA 0.5 LOG 1 !dpmaLNKS STATADAP RCON

CALCUL TINI 0. TEND 100.D-3*=================================================================PLAYCAME 1 EYE 5.00000E+00 5.00000E+00 3.53995E+01! Q 1.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00

VIEW 0.00000E+00 0.00000E+00 -1.00000E+00RIGH 1.00000E+00 0.00000E+00 0.00000E+00UP 0.00000E+00 1.00000E+00 0.00000E+00FOV 2.48819E+01

SCEN OBJE SELV FLSRGEOM NAVI FREEFACE HFROFLSR DOMACOLO PAPE

SLER CAM1 1 NFRA 1

TRAC OFFS FICH AVI NOCL NFTO 962 FPS 15 KFRE 10 COMP -1 RENDFREQ 1 !FREQ 0 TFRE 1.E-3GOTR LOOP 960 OFFS FICH AVI CONT NOCL RENDGOTRAC OFFS FICH AVI CONT RENDENDPLAY*=================================================================SUITPost-treatmentECHORESU ALIC GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'COUR 1 'dx_pcs' DEPL COMP 1 NOEU LECT 126 TERMCOUR 2 'vx_pcs' VITE COMP 1 NOEU LECT 126 TERMTRAC 1 AXES 1.0 'DISPL. [M]'TRAC 2 AXES 1.0 'VELOC. [M/S]'LIST 1 AXES 1.0 'DISPL. [M]'LIST 2 AXES 1.0 'VELOC. [M/S]'*=================================================================FIN

fsia06p.epx FSIA06PECHORESU ALIC 'fsia06.ali' GARD PSCROPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 5.00000E+00 3.53995E+01! Q 1.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00


SCEN GEOM NAVI FREEISO FILL FIEL ECRO 1 SCAL USER PROG 0.8E5 PAS 0.05E5 1.45E5 TERM

SUPP LECT flui TERMTEXT ISCACOLO PAPE

SLER CAM1 1 NFRA 1TRAC OFFS FICH AVI NOCL NFTO 962 FPS 15 KFRE 10 COMP -1 RENDFREQ 1GOTR LOOP 960 OFFS FICH AVI CONT NOCL RENDGOTRAC OFFS FICH AVI CONT RENDENDPLAY*=================================================================FIN

fsia06v.epx FSIA06VECHORESU ALIC 'fsia06.ali' GARD PSCROPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 5.00000E+00 3.53995E+01! Q 1.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00


SCEN GEOM NAVI FREEFACE HFROVECT SCCO FIEL VITE SCAL USER PROG 10 PAS 10 140 TERMTEXT VSCACOLO PAPE




TERMGEOM LIBR POIN 129 FL24 100 ED01 7 TERM0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 00 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 10 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 20 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 3 10 30 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 4 10 40 5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 10 50 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 9 6 10 60 7 1 7 2 7 3 7 4 7 5 7 6 7 7 7 8 7 9 7 10 70 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 8 9 8 10 80 9 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 9 10 90 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 101.5 1.5 1.5 2.5 1.5 3.5 1.5 4.51.5 5.5 1.5 6.5 1.5 7.5 1.5 8.51 2 13 12 2 3 14 13 3 4 15 14 4 5 16 15 5 6 17 166 7 18 17 7 8 19 18 8 9 20 19 9 10 21 20 10 11 22 2112 13 24 23 13 14 25 24 14 15 26 25 15 16 27 26 16 17 28 2717 18 29 28 18 19 30 29 19 20 31 30 20 21 32 31 21 22 33 3223 24 35 34 24 25 36 35 25 26 37 36 26 27 38 37 27 28 39 38

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28 29 40 39 29 30 41 40 30 31 42 41 31 32 43 42 32 33 44 4334 35 46 45 35 36 47 46 36 37 48 47 37 38 49 48 38 39 50 4939 40 51 50 40 41 52 51 41 42 53 52 42 43 54 53 43 44 55 5445 46 57 56 46 47 58 57 47 48 59 58 48 49 60 59 49 50 61 6050 51 62 61 51 52 63 62 52 53 64 63 53 54 65 64 54 55 66 6556 57 68 67 57 58 69 68 58 59 70 69 59 60 71 70 60 61 72 7161 62 73 72 62 63 74 73 63 64 75 74 64 65 76 75 65 66 77 7667 68 79 78 68 69 80 79 69 70 81 80 70 71 82 81 71 72 83 8272 73 84 83 73 74 85 84 74 75 86 85 75 76 87 86 76 77 88 8778 79 90 89 79 80 91 90 80 81 92 91 81 82 93 92 82 83 94 9383 84 95 94 84 85 96 95 85 86 97 96 86 87 98 97 87 88 99 9889 90 101 100 90 91 102 101 91 92 103 102 92 93 104 10393 94 105 104 94 95 106 105 95 96 107 106 96 97 108 10797 98 109 108 98 99 110 109100 101 112 111 101 102 113 112 102 103 114 113 103 104 115 114104 105 116 115 105 106 117 116 106 107 118 117 107 108 119 118108 109 120 119 109 110 121 120122 123 123 124 124 125 125 126 126 127127 128 128 129










!BFLU 0 FSCP 1BFLU 0 FSCP 0ADAP LMAX 4







SLER CAM1 1 NFRA 1TRAC OFFS FICH AVI NOCL NFTO 1124 FPS 15 KFRE 10 COMP -1 RENDFREQ 1 !FREQ 0 TFRE 1.E-3GOTR LOOP 1122 OFFS FICH AVI CONT NOCL RENDGOTRAC OFFS FICH AVI CONT RENDENDPLAY*=================================================================SUITPost-treatmentECHORESU ALIC GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'COUR 1 'dx_pcs' DEPL COMP 1 NOEU LECT 126 TERMCOUR 2 'vx_pcs' VITE COMP 1 NOEU LECT 126 TERMTRAC 1 AXES 1.0 'DISPL. [M]'TRAC 2 AXES 1.0 'VELOC. [M/S]'LIST 1 AXES 1.0 'DISPL. [M]'LIST 2 AXES 1.0 'VELOC. [M/S]'*=================================================================FIN





SLER CAM1 1 NFRA 1TRAC OFFS FICH AVI NOCL NFTO 1124 FPS 15 KFRE 10 COMP -1 RENDFREQ 1GOTR LOOP 1122 OFFS FICH AVI CONT NOCL REND

GOTRAC OFFS FICH AVI CONT RENDENDPLAY*=================================================================FIN







TERMGEOM LIBR POIN 129 FL24 100 ED01 7 TERM0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 00 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 10 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 20 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 3 10 30 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 4 10 40 5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 10 50 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 9 6 10 60 7 1 7 2 7 3 7 4 7 5 7 6 7 7 7 8 7 9 7 10 70 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 8 9 8 10 80 9 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 9 10 90 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 101.5 1.5 1.5 2.5 1.5 3.5 1.5 4.51.5 5.5 1.5 6.5 1.5 7.5 1.5 8.51 2 13 12 2 3 14 13 3 4 15 14 4 5 16 15 5 6 17 166 7 18 17 7 8 19 18 8 9 20 19 9 10 21 20 10 11 22 2112 13 24 23 13 14 25 24 14 15 26 25 15 16 27 26 16 17 28 2717 18 29 28 18 19 30 29 19 20 31 30 20 21 32 31 21 22 33 3223 24 35 34 24 25 36 35 25 26 37 36 26 27 38 37 27 28 39 3828 29 40 39 29 30 41 40 30 31 42 41 31 32 43 42 32 33 44 4334 35 46 45 35 36 47 46 36 37 48 47 37 38 49 48 38 39 50 4939 40 51 50 40 41 52 51 41 42 53 52 42 43 54 53 43 44 55 5445 46 57 56 46 47 58 57 47 48 59 58 48 49 60 59 49 50 61 6050 51 62 61 51 52 63 62 52 53 64 63 53 54 65 64 54 55 66 6556 57 68 67 57 58 69 68 58 59 70 69 59 60 71 70 60 61 72 7161 62 73 72 62 63 74 73 63 64 75 74 64 65 76 75 65 66 77 7667 68 79 78 68 69 80 79 69 70 81 80 70 71 82 81 71 72 83 8272 73 84 83 73 74 85 84 74 75 86 85 75 76 87 86 76 77 88 8778 79 90 89 79 80 91 90 80 81 92 91 81 82 93 92 82 83 94 9383 84 95 94 84 85 96 95 85 86 97 96 86 87 98 97 87 88 99 9889 90 101 100 90 91 102 101 91 92 103 102 92 93 104 10393 94 105 104 94 95 106 105 95 96 107 106 96 97 108 10797 98 109 108 98 99 110 109100 101 112 111 101 102 113 112 102 103 114 113 103 104 115 114104 105 116 115 105 106 117 116 106 107 118 117 107 108 119 118108 109 120 119 109 110 121 120122 123 123 124 124 125 125 126 126 127127 128 128 129









FLUI LECT flui TERMR 0.7072 ! so that d = 2r = 1.4144HGRI 1.6DGRI!BFLU 0 FSCP 1BFLU 0 FSCP 0ADAP LMAX 4 SCAL 2.0


Page 63



FICH ALIC FREQ 1 !TFRE 1.E-3OPTI NOTECSTA 0.5 LOG 1 !dpmaLNKS STAT

!ADAP RCONCALCUL TINI 0. TEND 100.D-3*=================================================================PLAYCAME 1 EYE 5.00000E+00 5.00000E+00 3.53995E+01! Q 1.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00













fsia11.dgibi opti echo 1;opti dime 2 elem qua4;opti titr 'FSIA11';opti sauv form 'fsia11.msh';opti trac psc ftra 'fsia11_mesh.ps';

p1 = 0 0;p2 = 10 0;p3 = 10 10;p4 = 0 10;n = 10;c1 = p1 d n p2;c2 = p2 d n p3;c3 = p3 d n p4;c4 = p4 d n p1;flui = dall c1 c2 c3 c4 plan;p1s = 1.5 1.5;pcs = 1.5 5.5;p2s = 1.5 8.5;ns1 = 4;ns2 = 3;stru = p1s d ns1 pcs d ns2 p2s;mesh = flui et stru;tass mesh;sauv form mesh;trac qual mesh;fin;

fsia11.epx FSIA11ECHO!CONV winCAST meshDPLA ALEDIME NALE 1 NBLE 1 TERMGEOM FL24 flui ED01 stru TERMCOMP NGRO 2 'blox' LECT c2 c4 TERM

'bloy' LECT c1 c3 TERMCOUL turq LECT flui TERM

vert LECT stru TERMEPAI 0.01 LECT stru TERM

GRIL LAGR LECT stru TERMEULE LECT flui TERM

MATE FLUT RO 1.0 EINT 2.5E5 GAMM 1.4 PB 0ITER 1 ALF0 1 BET0 1 KINT 0 AHGF 0 CL 0.5CQ 2.56 PMIN 0 NUM 1 PREF 1.E5LECT flui TERM



FLUI LECT flui TERMR 0.7072 ! so that d = 2r = 1.4144HGRI 1.6DGRI!BFLU 0 FSCP 1BFLU 0 FSCP 0







SLER CAM1 1 NFRA 1TRAC OFFS FICH AVI NOCL NFTO 962 FPS 15 KFRE 10 COMP -1 RENDFREQ 1 !FREQ 0 TFRE 1.E-3GOTR LOOP 960 OFFS FICH AVI CONT NOCL RENDGOTRAC OFFS FICH AVI CONT RENDENDPLAY*=================================================================SUITPost-treatmentECHORESU ALIC GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'COUR 1 'dx_pcs' DEPL COMP 1 NOEU LECT pcs TERMCOUR 2 'vx_pcs' VITE COMP 1 NOEU LECT pcs TERMTRAC 1 AXES 1.0 'DISPL. [M]'TRAC 2 AXES 1.0 'VELOC. [M/S]'LIST 1 AXES 1.0 'DISPL. [M]'LIST 2 AXES 1.0 'VELOC. [M/S]'*=================================================================FIN


VIEW 0.00000E+00 0.00000E+00 -1.00000E+00RIGH 1.00000E+00 0.00000E+00 0.00000E+00

Page 64

fsia11v.epx 28 February 2014 9:04 am

UP 0.00000E+00 1.00000E+00 0.00000E+00FOV 2.48819E+01








fsia12.dgibi opti echo 1;opti dime 2 elem qua4;opti titr 'FSIA12';opti sauv form 'fsia12.msh';opti trac psc ftra 'fsia12_mesh.ps';p1 = 0 0;p2 = 10 0;p3 = 10 10;p4 = 0 10;n = 20;c1 = p1 d n p2;c2 = p2 d n p3;c3 = p3 d n p4;c4 = p4 d n p1;flui = dall c1 c2 c3 c4 plan;p1s = 1.5 1.5;pcs = 1.5 5.5;p2s = 1.5 8.5;ns1 = 4;ns2 = 3;stru = p1s d ns1 pcs d ns2 p2s;mesh = flui et stru;tass mesh;sauv form mesh;trac qual mesh;fin;









!BFLU 0 FSCP 1BFLU 0 FSCP 0

















fsia13.dgibi opti echo 1;opti dime 2 elem qua4;opti titr 'FSIA13';opti sauv form 'fsia13.msh';opti trac psc ftra 'fsia13_mesh.ps';p1 = 0 0;

Page 65


p2 = 10 0;p3 = 10 10;p4 = 0 10;n = 40;c1 = p1 d n p2;c2 = p2 d n p3;c3 = p3 d n p4;c4 = p4 d n p1;flui = dall c1 c2 c3 c4 plan;p1s = 1.5 1.5;pcs = 1.5 5.5;p2s = 1.5 8.5;ns1 = 4;ns2 = 3;stru = p1s d ns1 pcs d ns2 p2s;mesh = flui et stru;tass mesh;sauv form mesh;trac qual mesh;fin;


















VIEW 0.00000E+00 0.00000E+00 -1.00000E+00RIGH 1.00000E+00 0.00000E+00 0.00000E+00UP 0.00000E+00 1.00000E+00 0.00000E+00

FOV 2.48819E+01SCEN GEOM NAVI FREE

ISO FILL FIEL ECRO 1 SCAL USER PROG 0.8E5 PAS 0.05E5 1.45E5 TERMSUPP LECT flui TERM

TEXT ISCACOLO PAPE
















POIN LECT stru TERM

Page 66

fsia14compare.epx 28 February 2014 9:04 am

ELEM LECT stru TERMFICH ALIC FREQ 1 !TFRE 1.E-3

OPTI NOTECSTA 0.5 LOG 1 !dpmaLNKS STAT





fsia14compare.epx FSIA14COMPAREECHORESU ALIC 'fsia14.ali' GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'RCOU 11 'dx_pcs' FICH 'fsia11.pun' RENA 'dx_pcs_11'RCOU 12 'vx_pcs' FICH 'fsia11.pun' RENA 'vx_pcs_11'RCOU 21 'dx_pcs' FICH 'fsia12.pun' RENA 'dx_pcs_12'RCOU 22 'vx_pcs' FICH 'fsia12.pun' RENA 'vx_pcs_12'RCOU 31 'dx_pcs' FICH 'fsia13.pun' RENA 'dx_pcs_13'RCOU 32 'vx_pcs' FICH 'fsia13.pun' RENA 'vx_pcs_13'RCOU 41 'dx_pcs' FICH 'fsia14.pun' RENA 'dx_pcs_14'RCOU 42 'vx_pcs' FICH 'fsia14.pun' RENA 'vx_pcs_14'RCOU 161 'dx_pcs' FICH 'fsia06.pun' RENA 'dx_pcs_06'RCOU 162 'vx_pcs' FICH 'fsia06.pun' RENA 'vx_pcs_06'RCOU 191 'dx_pcs' FICH 'fsia09.pun' RENA 'dx_pcs_09'RCOU 192 'vx_pcs' FICH 'fsia09.pun' RENA 'vx_pcs_09'RCOU 201 'dx_pcs' FICH 'fsia10.pun' RENA 'dx_pcs_10'RCOU 202 'vx_pcs' FICH 'fsia10.pun' RENA 'vx_pcs_10'TRAC 11 21 31 41 AXES 1.0 'DISPL. [M]'COLO NOIR BLEU TURQ VERTTRAC 12 22 32 42 AXES 1.0 'VELOC. [M/S]'COLO NOIR BLEU TURQ VERTTRAC 11 21 31 41 161 191 AXES 1.0 'DISPL. [M]'COLO NOIR BLEU TURQ VERT ROSE ROUGTRAC 12 22 32 42 162 192 AXES 1.0 'VELOC. [M/S]'COLO NOIR BLEU TURQ VERT ROSE ROUGTRAC 41 191 AXES 1.0 'DISPL. [M]'COLO VERT ROUGTRAC 42 192 AXES 1.0 'VELOC. [M/S]'COLO VERT ROUGTRAC 41 201 AXES 1.0 'DISPL. [M]'COLO VERT ROUGTRAC 42 202 AXES 1.0 'VELOC. [M/S]'COLO VERT ROUG*=================================================================FIN



SCEN GEOM NAVI FREELINE HEOU SFREISO FILL FIEL ECRO 1 SCAL USER PROG 0.8E5 PAS 0.05E5 1.45E5 TERM








ADAP NPOI 205 Q4VF 232 NVFI 526 ENDANALE 1 NBLE 1

TERMGEOM LIBR POIN 129 Q4VF 100 ED01 7 TERM0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 00 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 10 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 20 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 3 10 30 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 4 10 40 5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 10 50 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 9 6 10 60 7 1 7 2 7 3 7 4 7 5 7 6 7 7 7 8 7 9 7 10 70 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 8 9 8 10 80 9 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 9 10 90 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 101.5 1.5 1.5 2.5 1.5 3.5 1.5 4.51.5 5.5 1.5 6.5 1.5 7.5 1.5 8.51 2 13 12 2 3 14 13 3 4 15 14 4 5 16 15 5 6 17 166 7 18 17 7 8 19 18 8 9 20 19 9 10 21 20 10 11 22 2112 13 24 23 13 14 25 24 14 15 26 25 15 16 27 26 16 17 28 2717 18 29 28 18 19 30 29 19 20 31 30 20 21 32 31 21 22 33 3223 24 35 34 24 25 36 35 25 26 37 36 26 27 38 37 27 28 39 3828 29 40 39 29 30 41 40 30 31 42 41 31 32 43 42 32 33 44 4334 35 46 45 35 36 47 46 36 37 48 47 37 38 49 48 38 39 50 4939 40 51 50 40 41 52 51 41 42 53 52 42 43 54 53 43 44 55 5445 46 57 56 46 47 58 57 47 48 59 58 48 49 60 59 49 50 61 6050 51 62 61 51 52 63 62 52 53 64 63 53 54 65 64 54 55 66 6556 57 68 67 57 58 69 68 58 59 70 69 59 60 71 70 60 61 72 7161 62 73 72 62 63 74 73 63 64 75 74 64 65 76 75 65 66 77 7667 68 79 78 68 69 80 79 69 70 81 80 70 71 82 81 71 72 83 8272 73 84 83 73 74 85 84 74 75 86 85 75 76 87 86 76 77 88 8778 79 90 89 79 80 91 90 80 81 92 91 81 82 93 92 82 83 94 9383 84 95 94 84 85 96 95 85 86 97 96 86 87 98 97 87 88 99 9889 90 101 100 90 91 102 101 91 92 103 102 92 93 104 10393 94 105 104 94 95 106 105 95 96 107 106 96 97 108 10797 98 109 108 98 99 110 109100 101 112 111 101 102 113 112 102 103 114 113 103 104 115 114104 105 116 115 105 106 117 116 106 107 118 117 107 108 119 118108 109 120 119 109 110 121 120122 123 123 124 124 125 125 126 126 127127 128 128 129





EULE LECT flui TERMMATE GAZP RO 1.0 GAMM 1.4 PINI 1.E5 PREF 1.E5

LECT flui _q4vf TERMVM23 RO 7800. YOUNG 1.6E11 NU 0.333 ELAS 1.05E8

TRAC 2 1.05E8 .656256E-3 1.6105E10 1.00066LECT stru TERM

LINK DECOFLSW STRU LECT stru TERM

FLUI LECT flui TERMR 0.7072 ! so that d = 2r = 1.4144HGRI 1.6DGRIFACEBFLU 1 FSCP 0ADAP LMAX 3

INIT VITE 1 100.0 LECT stru TERMECRI DEPL VITE ACCE FINT FEXT VFCC TFRE 10.E-3



CALCUL TINI 0. TEND 100.D-3*=================================================================PLAYCAME 1 EYE 5.00000E+00 5.00000E+00 3.53995E+01

Page 67


! Q 1.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00VIEW 0.00000E+00 0.00000E+00 -1.00000E+00RIGH 1.00000E+00 0.00000E+00 0.00000E+00UP 0.00000E+00 1.00000E+00 0.00000E+00FOV 2.48819E+01

SCEN OBJE !SELV FLSWGEOM NAVI FREEFACE HFROFLSW DOMACOLO PAPE









SCEN GEOM NAVI FREEFACE HFROVECT SCCO FIEL VCVI SCAL USER PROG 10 PAS 10 140 TERM

SUPP LECT flui TERMTEXT VSCACOLO PAPE




TERMGEOM LIBR POIN 129 Q4VF 100 ED01 7 TERM0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 00 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 10 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 20 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 3 10 30 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 4 10 40 5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 10 5

0 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 9 6 10 60 7 1 7 2 7 3 7 4 7 5 7 6 7 7 7 8 7 9 7 10 70 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 8 9 8 10 80 9 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 9 10 90 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 101.5 1.5 1.5 2.5 1.5 3.5 1.5 4.51.5 5.5 1.5 6.5 1.5 7.5 1.5 8.51 2 13 12 2 3 14 13 3 4 15 14 4 5 16 15 5 6 17 166 7 18 17 7 8 19 18 8 9 20 19 9 10 21 20 10 11 22 2112 13 24 23 13 14 25 24 14 15 26 25 15 16 27 26 16 17 28 2717 18 29 28 18 19 30 29 19 20 31 30 20 21 32 31 21 22 33 3223 24 35 34 24 25 36 35 25 26 37 36 26 27 38 37 27 28 39 3828 29 40 39 29 30 41 40 30 31 42 41 31 32 43 42 32 33 44 4334 35 46 45 35 36 47 46 36 37 48 47 37 38 49 48 38 39 50 4939 40 51 50 40 41 52 51 41 42 53 52 42 43 54 53 43 44 55 5445 46 57 56 46 47 58 57 47 48 59 58 48 49 60 59 49 50 61 6050 51 62 61 51 52 63 62 52 53 64 63 53 54 65 64 54 55 66 6556 57 68 67 57 58 69 68 58 59 70 69 59 60 71 70 60 61 72 7161 62 73 72 62 63 74 73 63 64 75 74 64 65 76 75 65 66 77 7667 68 79 78 68 69 80 79 69 70 81 80 70 71 82 81 71 72 83 8272 73 84 83 73 74 85 84 74 75 86 85 75 76 87 86 76 77 88 8778 79 90 89 79 80 91 90 80 81 92 91 81 82 93 92 82 83 94 9383 84 95 94 84 85 96 95 85 86 97 96 86 87 98 97 87 88 99 9889 90 101 100 90 91 102 101 91 92 103 102 92 93 104 10393 94 105 104 94 95 106 105 95 96 107 106 96 97 108 10797 98 109 108 98 99 110 109100 101 112 111 101 102 113 112 102 103 114 113 103 104 115 114104 105 116 115 105 106 117 116 106 107 118 117 107 108 119 118108 109 120 119 109 110 121 120122 123 123 124 124 125 125 126 126 127127 128 128 129



















SCEN GEOM NAVI FREE

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TEXT ISCACOLO PAPE









TERMGEOM LIBR POIN 129 Q4VF 100 ED01 7 TERM0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 00 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 10 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 20 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 3 10 30 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 4 10 40 5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 10 50 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 9 6 10 60 7 1 7 2 7 3 7 4 7 5 7 6 7 7 7 8 7 9 7 10 70 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 8 9 8 10 80 9 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 9 10 90 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 101.5 1.5 1.5 2.5 1.5 3.5 1.5 4.51.5 5.5 1.5 6.5 1.5 7.5 1.5 8.51 2 13 12 2 3 14 13 3 4 15 14 4 5 16 15 5 6 17 166 7 18 17 7 8 19 18 8 9 20 19 9 10 21 20 10 11 22 2112 13 24 23 13 14 25 24 14 15 26 25 15 16 27 26 16 17 28 2717 18 29 28 18 19 30 29 19 20 31 30 20 21 32 31 21 22 33 3223 24 35 34 24 25 36 35 25 26 37 36 26 27 38 37 27 28 39 3828 29 40 39 29 30 41 40 30 31 42 41 31 32 43 42 32 33 44 4334 35 46 45 35 36 47 46 36 37 48 47 37 38 49 48 38 39 50 4939 40 51 50 40 41 52 51 41 42 53 52 42 43 54 53 43 44 55 5445 46 57 56 46 47 58 57 47 48 59 58 48 49 60 59 49 50 61 6050 51 62 61 51 52 63 62 52 53 64 63 53 54 65 64 54 55 66 6556 57 68 67 57 58 69 68 58 59 70 69 59 60 71 70 60 61 72 7161 62 73 72 62 63 74 73 63 64 75 74 64 65 76 75 65 66 77 7667 68 79 78 68 69 80 79 69 70 81 80 70 71 82 81 71 72 83 8272 73 84 83 73 74 85 84 74 75 86 85 75 76 87 86 76 77 88 8778 79 90 89 79 80 91 90 80 81 92 91 81 82 93 92 82 83 94 9383 84 95 94 84 85 96 95 85 86 97 96 86 87 98 97 87 88 99 9889 90 101 100 90 91 102 101 91 92 103 102 92 93 104 10393 94 105 104 94 95 106 105 95 96 107 106 96 97 108 10797 98 109 108 98 99 110 109100 101 112 111 101 102 113 112 102 103 114 113 103 104 115 114104 105 116 115 105 106 117 116 106 107 118 117 107 108 119 118108 109 120 119 109 110 121 120122 123 123 124 124 125 125 126 126 127127 128 128 129










FACEBFLU 1 FSCP 0ADAP LMAX 4 SCAL 2.0


















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fsia21.dgibi 28 February 2014 9:04 am


fsia21.epx FSIA21ECHO!CONV winCAST meshDPLA ALEDIME NALE 1 NBLE 1 TERMGEOM Q4VF flui ED01 stru TERMCOMP NGRO 2 'blox' LECT c2 c4 TERM




MATE GAZP RO 1.0 GAMM 1.4 PINI 1.E5 PREF 1.E5LECT flui TERM



FLUI LECT flui TERMR 0.7072 ! so that d = 2r = 1.4144HGRI 1.6DGRIFACEBFLU 1 FSCP 0








fsia21p.epx FSIA21PECHORESU ALIC 'fsia21.ali' GARD PSCROPTI PRINSORT VISU NSTO 1*=================================================================PLAY

CAME 1 EYE 5.00000E+00 5.00000E+00 3.53995E+01! Q 1.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00



















INIT VITE 1 100.0 LECT stru TERM

Page 70


ECRI DEPL VITE ACCE FINT FEXT VFCC TFRE 10.E-3POIN LECT stru TERMELEM LECT stru TERM
















fsia23.dgibi opti echo 1;opti dime 2 elem qua4;opti titr 'FSIA23';opti sauv form 'fsia23.msh';

opti trac psc ftra 'fsia23_mesh.ps';p1 = 0 0;p2 = 10 0;p3 = 10 10;p4 = 0 10;n = 40;c1 = p1 d n p2;c2 = p2 d n p3;c3 = p3 d n p4;c4 = p4 d n p1;flui = dall c1 c2 c3 c4 plan;p1s = 1.5 1.5;pcs = 1.5 5.5;p2s = 1.5 8.5;ns1 = 4;ns2 = 3;stru = p1s d ns1 pcs d ns2 p2s;mesh = flui et stru;tass mesh;sauv form mesh;trac qual mesh;fin;


















SCEN GEOM NAVI FREE

Page 71



TEXT ISCACOLO PAPE























fsia24compare.epx FSIA24COMPAREECHORESU ALIC 'fsia24.ali' GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'RCOU 11 'dx_pcs' FICH 'fsia21.pun' RENA 'dx_pcs_21'RCOU 12 'vx_pcs' FICH 'fsia21.pun' RENA 'vx_pcs_21'RCOU 21 'dx_pcs' FICH 'fsia22.pun' RENA 'dx_pcs_22'RCOU 22 'vx_pcs' FICH 'fsia22.pun' RENA 'vx_pcs_22'RCOU 31 'dx_pcs' FICH 'fsia23.pun' RENA 'dx_pcs_23'RCOU 32 'vx_pcs' FICH 'fsia23.pun' RENA 'vx_pcs_23'RCOU 41 'dx_pcs' FICH 'fsia24.pun' RENA 'dx_pcs_24'RCOU 42 'vx_pcs' FICH 'fsia24.pun' RENA 'vx_pcs_24'RCOU 161 'dx_pcs' FICH 'fsia16.pun' RENA 'dx_pcs_16'RCOU 162 'vx_pcs' FICH 'fsia16.pun' RENA 'vx_pcs_16'RCOU 191 'dx_pcs' FICH 'fsia19.pun' RENA 'dx_pcs_19'RCOU 192 'vx_pcs' FICH 'fsia19.pun' RENA 'vx_pcs_19'RCOU 201 'dx_pcs' FICH 'fsia20.pun' RENA 'dx_pcs_20'RCOU 202 'vx_pcs' FICH 'fsia20.pun' RENA 'vx_pcs_20'RCOU 141 'dx_pcs' FICH 'fsia14.pun' RENA 'dx_pcs_14' ! FERCOU 142 'vx_pcs' FICH 'fsia14.pun' RENA 'vx_pcs_14' ! FETRAC 11 21 31 41 AXES 1.0 'DISPL. [M]'COLO NOIR BLEU TURQ VERTTRAC 12 22 32 42 AXES 1.0 'VELOC. [M/S]'COLO NOIR BLEU TURQ VERTTRAC 11 21 31 41 161 191 AXES 1.0 'DISPL. [M]'COLO NOIR BLEU TURQ VERT ROSE ROUGTRAC 12 22 32 42 162 192 AXES 1.0 'VELOC. [M/S]'COLO NOIR BLEU TURQ VERT ROSE ROUGTRAC 41 191 AXES 1.0 'DISPL. [M]'COLO VERT ROUGTRAC 42 192 AXES 1.0 'VELOC. [M/S]'COLO VERT ROUGTRAC 41 141 AXES 1.0 'DISPL. [M]'COLO VERT ROUGTRAC 42 142 AXES 1.0 'VELOC. [M/S]'COLO VERT ROUGTRAC 41 201 AXES 1.0 'DISPL. [M]'COLO VERT ROUGTRAC 42 202 AXES 1.0 'VELOC. [M/S]'COLO VERT ROUG*=================================================================FIN



SCEN GEOM NAVI FREELINE HEOU SFREISO FILL FIEL ECRO 1 SCAL USER PROG 0.8E5 PAS 0.05E5 1.45E5 TERM



Page 72







fsia26.dgibi opti echo 1;opti dime 3 elem cub8;opti titr 'FSIA26';opti sauv form 'fsia26.msh';opti trac psc ftra 'fsia26_mesh.ps';p1 = 0 0 0;p2 = 10 0 0;p3 = 10 10 0;p4 = 0 10 0;pz = 0 0 10;n = 10;c1 = p1 d n p2;c2 = p2 d n p3;c3 = p3 d n p4;c4 = p4 d n p1;base = dall c1 c2 c3 c4 plan;flui = base volu tran n pz;fsrn = enve flui;p1s = 1.5 1.5 1.5;pcs = 1.5 5.5 1.5;p2s = 1.5 8.5 1.5;pzs = 0 0 7;ns1 = 4;ns2 = 3;bstru = p1s d ns1 pcs d ns2 p2s;stru = bstru tran (ns1+ns2) pzs;mesh = flui et stru et fsrn;tass mesh;sauv form mesh;trac mesh;trac cach qual mesh;fin;

fsia26.epx FSIA26ECHO!CONV winCAST meshTRID ALEDIME


TERMGEOM FL38 flui Q4GS stru TERMCOMP NGRO 1 'cs' LECT stru TERM COND NEAR POIN 1.5 5 5






LINK COUPFSR LECT fsrn TERMFLSR STRU LECT stru TERM

FLUI LECT flui TERMR 0.87 ! so that d = 2r = 1.74HGRI 1.6DGRIBFLU 0 FSCP 0ADAP LMAX 3



FICH SPLI ALIC FREQ 1 !TFRE 1.E-3OPTI NOTECSTA 0.5 LOG 1 !dpmaLNKS STATADAP RCON

CALCUL TINI 0. TEND 100.D-3FIN

fsia26a.epx FSIA26AECHORESU SPLI ALIC 'fsia26.ali' GARD PSCRCOMP NGRO 1 'cs' LECT stru TERM COND NEAR POIN 1.5 5 5SORT GRAPPERF 'fsia26.pun'AXTE 1.0 'Time [s]'COUR 1 'dx_cs' DEPL COMP 1 NOEU LECT cs TERMCOUR 2 'vx_cs' VITE COMP 1 NOEU LECT cs TERMTRAC 1 AXES 1.0 'DISPL. [M]'TRAC 2 AXES 1.0 'VELOC. [M/S]'LIST 1 AXES 1.0 'DISPL. [M]'LIST 2 AXES 1.0 'VELOC. [M/S]'*=================================================================FIN

fsia26b.epx FSIA26BECHORESU SPLI ALIC 'fsia26.ali' GARD PSCROPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 -3.68258E+01 1.62072E+01! Q 7.93353E-01 6.08761E-01 4.52854E-19 3.43977E-18

VIEW -4.90654E-18 9.65926E-01 -2.58819E-01RIGH 1.00000E+00 6.00926E-18 3.46945E-18UP -4.90654E-18 2.58819E-01 9.65926E-01FOV 2.48819E+01

!NAVIGATION MODE: ROTATING CAMERA!CENTER : 5.00000E+00 5.00000E+00 5.00000E+00!RSPHERE: 8.66025E+00!RADIUS : 4.33013E+01!ASPECT : 1.00000E+00!NEAR : 3.37750E+01!FAR : 6.06218E+01SCEN OBJE !SELV FLSR

!USLM LECT flui TERM DHAS CGLAGEOM NAVI FREE

REFE BBOXFACE HFROLINE HEOU SFREFLSR DOMACOLO PAPE

SLER CAM1 1 NFRA 1TRAC OFFS FICH AVI NOCL NFTO 967 FPS 15 KFRE 10 COMP -1 RENDFREQ 1 !FREQ 0 TFRE 1.E-3GOTR LOOP 965 OFFS FICH AVI CONT NOCL RENDGOTRAC OFFS FICH AVI CONT RENDENDPLAY*=================================================================FIN

fsia26p.epx FSIA26PECHORESU SPLI ALIC 'fsia26.ali' GARD PSCR!COMP GROU 1 'ygt5' LECT tous TERM COND YB GT 4.9OPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 -3.68258E+01 1.62072E+01! Q 7.93353E-01 6.08761E-01 4.52854E-19 3.43977E-18


!NAVIGATION MODE: ROTATING CAMERA!CENTER : 5.00000E+00 5.00000E+00 5.00000E+00!RSPHERE: 8.66025E+00!RADIUS : 4.33013E+01!ASPECT : 1.00000E+00!NEAR : 3.37750E+01!FAR : 6.06218E+01SCEN GEOM NAVI FREE


TEXT ISCACOLO PAPE

SLER CAM1 1 NFRA 1TRAC OFFS FICH AVI NOCL NFTO 967 FPS 15 KFRE 10 COMP -1! OBJE LECT ygt5 TERM REND

RENDFREQ 1GOTR LOOP 965 OFFS FICH AVI CONT NOCL! OBJE LECT ygt5 TERM REND

RENDGOTRAC OFFS FICH AVI CONT! OBJE LECT ygt5 TERM REND

RENDENDPLAY*=================================================================FIN

fsia26v.epx FSIA26VECHORESU SPLI ALIC 'fsia26.ali' GARD PSCR!COMP GROU 1 'ygt5' LECT tous TERM COND YB GT 4.9OPTI PRIN

Page 73


SORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 -3.68258E+01 1.62072E+01! Q 7.93353E-01 6.08761E-01 4.52854E-19 3.43977E-18



FACE HFROVECT SCCO FIEL VITE SCAL USER PROG 10 PAS 10 140 TERM

SIVETEXT VSCACOLO PAPE




RENDENDPLAY*=================================================================FIN


fsia31.epx FSIA31ECHO!CONV winCAST meshTRID ALEDIME NALE 1 NBLE 1 TERMGEOM FL38 flui Q4GS stru TERMCOMP NGRO 1 'cs' LECT stru TERM COND NEAR POIN 1.5 5 5




ITER 1 ALF0 1 BET0 1 KINT 0 AHGF 0 CL 0.5CQ 2.56 PMIN 0 NUM 1 PREF 1.E5LECT flui TERM








CALCUL TINI 0. TEND 100.D-3

*=================================================================PLAYCAME 1 EYE 5.00000E+00 -3.68258E+01 1.62072E+01! Q 7.93353E-01 6.08761E-01 4.52854E-19 3.43977E-18


!NAVIGATION MODE: ROTATING CAMERA!CENTER : 5.00000E+00 5.00000E+00 5.00000E+00!RSPHERE: 8.66025E+00!RADIUS : 4.33013E+01!ASPECT : 1.00000E+00!NEAR : 3.37750E+01!FAR : 6.06218E+01SCEN OBJE SELV FLSR

GEOM NAVI FREEFACE HFROLINE HEOU SSHA SFREFLSR DOMACOLO PAPE

SLER CAM1 1 NFRA 1TRAC OFFS FICH AVI NOCL NFTO 967 FPS 15 KFRE 10 COMP -1 RENDFREQ 1 !FREQ 0 TFRE 1.E-3GOTR LOOP 965 OFFS FICH AVI CONT NOCL RENDGOTRAC OFFS FICH AVI CONT RENDENDPLAY*=================================================================SUITPost-treatmentECHORESU ALIC GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'COUR 1 'dx_cs' DEPL COMP 1 NOEU LECT cs TERMCOUR 2 'vx_cs' VITE COMP 1 NOEU LECT cs TERMTRAC 1 AXES 1.0 'DISPL. [M]'TRAC 2 AXES 1.0 'VELOC. [M/S]'LIST 1 AXES 1.0 'DISPL. [M]'LIST 2 AXES 1.0 'VELOC. [M/S]'*=================================================================FIN

fsia31p.epx FSIA31PECHORESU ALIC 'fsia31.ali' GARD PSCRCOMP GROU 1 'ygt5' LECT tous TERM COND YB GT 4.9OPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 -3.68258E+01 1.62072E+01! Q 7.93353E-01 6.08761E-01 4.52854E-19 3.43977E-18




TEXT ISCACOLO PAPE

SLER CAM1 1 NFRA 1TRAC OFFS FICH AVI NOCL NFTO 967 FPS 15 KFRE 10 COMP -1

OBJE LECT ygt5 TERM RENDFREQ 1GOTR LOOP 965 OFFS FICH AVI CONT NOCL

OBJE LECT ygt5 TERM RENDGOTRAC OFFS FICH AVI CONT

OBJE LECT ygt5 TERM RENDENDPLAY*=================================================================FIN

fsia31v.epx FSIA31VECHORESU ALIC 'fsia31.ali' GARD PSCRCOMP GROU 1 'ygt5' LECT tous TERM COND YB GT 4.9OPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 -3.68258E+01 1.62072E+01! Q 7.93353E-01 6.08761E-01 4.52854E-19 3.43977E-18




SIVETEXT VSCA

Page 74


COLO PAPESLER CAM1 1 NFRA 1TRAC OFFS FICH AVI NOCL NFTO 967 FPS 15 KFRE 10 COMP -1

















CALCUL TINI 0. TEND 100.D-3*=================================================================PLAYCAME 1 EYE 5.00000E+00 -3.68258E+01 1.62072E+01! Q 7.93353E-01 6.08761E-01 4.52854E-19 3.43977E-18



GEOM NAVI FREEFACE HFROLINE HEOU SSHA SFREFLSR DOMACOLO PAPE

SLER CAM1 1 NFRA 1TRAC OFFS FICH AVI NOCL NFTO 963 FPS 15 KFRE 10 COMP -1 RENDFREQ 1 !FREQ 0 TFRE 1.E-3

GOTR LOOP 961 OFFS FICH AVI CONT NOCL RENDGOTRAC OFFS FICH AVI CONT RENDENDPLAY*=================================================================SUITPost-treatmentECHORESU ALIC GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'COUR 1 'dx_cs' DEPL COMP 1 NOEU LECT cs TERMCOUR 2 'vx_cs' VITE COMP 1 NOEU LECT cs TERMTRAC 1 AXES 1.0 'DISPL. [M]'TRAC 2 AXES 1.0 'VELOC. [M/S]'LIST 1 AXES 1.0 'DISPL. [M]'LIST 2 AXES 1.0 'VELOC. [M/S]'*=================================================================FIN





TEXT ISCACOLO PAPE














fsia33.dgibi opti echo 1;opti dime 3 elem cub8;opti titr 'FSIA33';opti sauv form 'fsia33.msh';opti trac psc ftra 'fsia33_mesh.ps';p1 = 0 0 0;

Page 75


p2 = 10 0 0;p3 = 10 10 0;p4 = 0 10 0;pz = 0 0 10;n = 40;c1 = p1 d n p2;c2 = p2 d n p3;c3 = p3 d n p4;c4 = p4 d n p1;base = dall c1 c2 c3 c4 plan;flui = base volu tran n pz;fsrn = enve flui;p1s = 1.5 1.5 1.5;pcs = 1.5 5.5 1.5;p2s = 1.5 8.5 1.5;pzs = 0 0 7;ns1 = 4;ns2 = 3;bstru = p1s d ns1 pcs d ns2 p2s;stru = bstru tran (ns1+ns2) pzs;mesh = flui et stru et fsrn;tass mesh;sauv form mesh;trac mesh;trac cach qual mesh;fin;








FLUI LECT flui TERMR 0.2175 ! so that d = 2r = 0.435HGRI 1.6DGRIBFLU 0 FSCP 0



FICH SPLI ALIC FREQ 1 !TFRE 1.E-3OPTI NOTECSTA 0.5 LOG 1 !dpmaLNKS STAT


fsia33a.epx FSIA33AECHORESU SPLI ALIC 'fsia33.ali' GARD PSCRCOMP NGRO 1 'cs' LECT stru TERM COND NEAR POIN 1.5 5 5SORT GRAPPERF 'fsia33.pun'AXTE 1.0 'Time [s]'COUR 1 'dx_cs' DEPL COMP 1 NOEU LECT cs TERMCOUR 2 'vx_cs' VITE COMP 1 NOEU LECT cs TERMTRAC 1 AXES 1.0 'DISPL. [M]'TRAC 2 AXES 1.0 'VELOC. [M/S]'LIST 1 AXES 1.0 'DISPL. [M]'LIST 2 AXES 1.0 'VELOC. [M/S]'*=================================================================FIN

fsia33b.epx FSIA33BECHORESU SPLI ALIC 'fsia33.ali' GARD PSCRCOMP GROU 1 'ygt5' LECT tous TERM COND YB GT 4.9OPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 -3.68258E+01 1.62072E+01! Q 7.93353E-01 6.08761E-01 4.52854E-19 3.43977E-18



GEOM NAVI FREE

FACE HFROLINE HEOU SSHA SFREFLSR DOMACOLO PAPE


fsia33compare.epx FSIA33COMPAREECHORESU SPLI ALIC 'fsia33.ali' GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'RCOU 11 'dx_cs' FICH 'fsia31.pun' RENA 'dx_cs_31'RCOU 12 'vx_cs' FICH 'fsia31.pun' RENA 'vx_cs_31'RCOU 21 'dx_cs' FICH 'fsia32.pun' RENA 'dx_cs_32'RCOU 22 'vx_cs' FICH 'fsia32.pun' RENA 'vx_cs_32'RCOU 31 'dx_cs' FICH 'fsia33.pun' RENA 'dx_cs_33'RCOU 32 'vx_cs' FICH 'fsia33.pun' RENA 'vx_cs_33'RCOU 161 'dx_cs' FICH 'fsia26.pun' RENA 'dx_ps_26'RCOU 162 'vx_cs' FICH 'fsia26.pun' RENA 'vx_ps_26'!RCOU 191 'dx_pcs' FICH 'fsia19.pun' RENA 'dx_pcs_19'!RCOU 192 'vx_pcs' FICH 'fsia19.pun' RENA 'vx_pcs_19'!RCOU 141 'dx_pcs' FICH 'fsia14.pun' RENA 'dx_pcs_14' ! FE!RCOU 142 'vx_pcs' FICH 'fsia14.pun' RENA 'vx_pcs_14' ! FETRAC 11 21 31 AXES 1.0 'DISPL. [M]'COLO NOIR BLEU TURQTRAC 12 22 32 AXES 1.0 'VELOC. [M/S]'COLO NOIR BLEU TURQTRAC 11 21 31 161 AXES 1.0 'DISPL. [M]'COLO NOIR BLEU TURQ ROUGTRAC 12 22 32 162 AXES 1.0 'VELOC. [M/S]'COLO NOIR BLEU TURQ ROUG!TRAC 41 191 AXES 1.0 'DISPL. [M]'!COLO VERT ROUG!TRAC 42 192 AXES 1.0 'VELOC. [M/S]'!COLO VERT ROUGTRAC 31 161 AXES 1.0 'DISPL. [M]'COLO TURQ ROUGTRAC 32 162 AXES 1.0 'VELOC. [M/S]'COLO TURQ ROUG*=================================================================FIN

fsia33p.epx FSIA33PECHORESU SPLI ALIC 'fsia33.ali' GARD PSCRCOMP GROU 1 'ygt5' LECT tous TERM COND YB GT 4.9OPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 -3.68258E+01 1.62072E+01! Q 7.93353E-01 6.08761E-01 4.52854E-19 3.43977E-18




TEXT ISCACOLO PAPE





fsia33v.epx FSIA33VECHORESU SPLI ALIC 'fsia33.ali' GARD PSCRCOMP GROU 1 'ygt5' LECT tous TERM COND YB GT 4.9OPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 -3.68258E+01 1.62072E+01! Q 7.93353E-01 6.08761E-01 4.52854E-19 3.43977E-18


!NAVIGATION MODE: ROTATING CAMERA!CENTER : 5.00000E+00 5.00000E+00 5.00000E+00

Page 76


!RSPHERE: 8.66025E+00!RADIUS : 4.33013E+01!ASPECT : 1.00000E+00!NEAR : 3.37750E+01!FAR : 6.06218E+01SCEN GEOM NAVI FREE

FACE HFROLINE HEOU SSHA SFREVECT SCCO FIEL VITE SCAL USER PROG 10 PAS 10 140 TERM







fsia36.epx FSIA36ECHO!CONV winCAST meshTRID ALEDIME

ADAP NPOI 10000 CUVF 10000 NVFI 100000 ENDANALE 1 NBLE 1

TERMGEOM CUVF flui Q4GS stru TERMCOMP NGRO 1 'cs' LECT stru TERM COND NEAR POIN 1.5 5 5




LECT flui _cuvf TERMVM23 RO 7800. YOUNG 1.6E11 NU 0.333 ELAS 1.05E8






FICH SPLI ALIC FREQ 1 !TFRE 1.E-3OPTI NOTECSTA 0.5 LOG 1 !dpmaLNKS STATADAP RCON


fsia36a.epx FSIA36AECHORESU SPLI ALIC 'fsia36.ali' GARD PSCRCOMP NGRO 1 'cs' LECT stru TERM COND NEAR POIN 1.5 5 5SORT GRAP

PERF 'fsia36.pun'AXTE 1.0 'Time [s]'COUR 1 'dx_cs' DEPL COMP 1 NOEU LECT cs TERMCOUR 2 'vx_cs' VITE COMP 1 NOEU LECT cs TERMTRAC 1 AXES 1.0 'DISPL. [M]'TRAC 2 AXES 1.0 'VELOC. [M/S]'LIST 1 AXES 1.0 'DISPL. [M]'LIST 2 AXES 1.0 'VELOC. [M/S]'*=================================================================FIN

fsia36b.epx FSIA36BECHORESU SPLI ALIC 'fsia36.ali' GARD PSCROPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 -3.68258E+01 1.62072E+01! Q 7.93353E-01 6.08761E-01 4.52854E-19 3.43977E-18


!NAVIGATION MODE: ROTATING CAMERA!CENTER : 5.00000E+00 5.00000E+00 5.00000E+00!RSPHERE: 8.66025E+00!RADIUS : 4.33013E+01!ASPECT : 1.00000E+00!NEAR : 3.37750E+01!FAR : 6.06218E+01SCEN OBJE !SELV FLSW

!USLM LECT flui TERM DHAS CGLAGEOM NAVI FREE

REFE BBOXFACE HFROLINE HEOU SFREFLSW DOMACOLO PAPE


fsia36p.epx FSIA36PECHORESU SPLI ALIC 'fsia36.ali' GARD PSCR!COMP GROU 1 'ygt5' LECT tous TERM COND YB GT 4.9OPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 -3.68258E+01 1.62072E+01! Q 7.93353E-01 6.08761E-01 4.52854E-19 3.43977E-18




TEXT ISCACOLO PAPE




RENDENDPLAY*=================================================================FIN

fsia36v.epx FSIA36VECHORESU SPLI ALIC 'fsia36.ali' GARD PSCR!COMP GROU 1 'ygt5' LECT tous TERM COND YB GT 4.9OPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 -3.68258E+01 1.62072E+01! Q 7.93353E-01 6.08761E-01 4.52854E-19 3.43977E-18


Page 77



FACE HFROVECT SCCO FIEL VCVI SCAL USER PROG 10 PAS 10 140 TERM

SUPP LECT flui TERMSIVE

TEXT VSCACOLO PAPE




RENDENDPLAY*=================================================================FIN


fsia41.epx FSIA41ECHO!CONV winCAST meshTRID ALEDIME NALE 1 NBLE 1 TERMGEOM CUVF flui Q4GS stru TERMCOMP NGRO 1 'cs' LECT stru TERM COND NEAR POIN 1.5 5 5




LECT flui TERMVM23 RO 7800. YOUNG 1.6E11 NU 0.333 ELAS 1.05E8








fsia41a.epx FSIA41AECHORESU ALIC 'fsia41.ali' GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'

COUR 1 'dx_cs' DEPL COMP 1 NOEU LECT cs TERMCOUR 2 'vx_cs' VITE COMP 1 NOEU LECT cs TERMTRAC 1 AXES 1.0 'DISPL. [M]'TRAC 2 AXES 1.0 'VELOC. [M/S]'LIST 1 AXES 1.0 'DISPL. [M]'LIST 2 AXES 1.0 'VELOC. [M/S]'FIN

fsia41b.epx FSIA41BECHORESU ALIC 'fsia41.ali' GARD PSCROPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 -3.68258E+01 1.62072E+01! Q 7.93353E-01 6.08761E-01 4.52854E-19 3.43977E-18


!NAVIGATION MODE: ROTATING CAMERA!CENTER : 5.00000E+00 5.00000E+00 5.00000E+00!RSPHERE: 8.66025E+00!RADIUS : 4.33013E+01!ASPECT : 1.00000E+00!NEAR : 3.37750E+01!FAR : 6.06218E+01SCEN OBJE SELV FLSW

GEOM NAVI FREEFACE HFROLINE HEOU SSHA SFREFLSW DOMACOLO PAPE






TEXT ISCACOLO PAPE








Page 78



SUPP LECT FLUI TERM SIVETEXT VSCACOLO PAPE


















fsia42a.epx FSIA42AECHORESU ALIC 'fsia42.ali' GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'COUR 1 'dx_cs' DEPL COMP 1 NOEU LECT cs TERMCOUR 2 'vx_cs' VITE COMP 1 NOEU LECT cs TERMTRAC 1 AXES 1.0 'DISPL. [M]'TRAC 2 AXES 1.0 'VELOC. [M/S]'LIST 1 AXES 1.0 'DISPL. [M]'LIST 2 AXES 1.0 'VELOC. [M/S]'FIN










TEXT ISCACOLO PAPE











OBJE LECT ygt5 TERM RENDFREQ 1

Page 79


GOTR LOOP 962 OFFS FICH AVI CONT NOCLOBJE LECT ygt5 TERM REND

GOTRAC OFFS FICH AVI CONT















fsia43a.epx FSIA43AECHORESU ALIC 'fsia43.ali' GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'COUR 1 'dx_cs' DEPL COMP 1 NOEU LECT cs TERMCOUR 2 'vx_cs' VITE COMP 1 NOEU LECT cs TERMTRAC 1 AXES 1.0 'DISPL. [M]'TRAC 2 AXES 1.0 'VELOC. [M/S]'LIST 1 AXES 1.0 'DISPL. [M]'LIST 2 AXES 1.0 'VELOC. [M/S]'FIN










TEXT ISCACOLO PAPE








FACE HFROLINE HEOU SSHA SFREVECT SCCO FIEL VCVI SCAL USER PROG 10 PAS 10 140 TERM






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mill04.epx MILL04ECHO!CONV winDPLA ALEDIME


TERMGEOM LIBR POIN 138 FL24 100 ED01 16 TERM0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 00 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 10 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 20 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 3 10 30 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 4 10 40 5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 10 50 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 9 6 10 60 7 1 7 2 7 3 7 4 7 5 7 6 7 7 7 8 7 9 7 10 70 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 8 9 8 10 80 9 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 9 10 90 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 105 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 91 5 2 5 3 5 4 5 6 5 7 5 8 5 9 51 2 13 12 2 3 14 13 3 4 15 14 4 5 16 15 5 6 17 166 7 18 17 7 8 19 18 8 9 20 19 9 10 21 20 10 11 22 2112 13 24 23 13 14 25 24 14 15 26 25 15 16 27 26 16 17 28 2717 18 29 28 18 19 30 29 19 20 31 30 20 21 32 31 21 22 33 3223 24 35 34 24 25 36 35 25 26 37 36 26 27 38 37 27 28 39 3828 29 40 39 29 30 41 40 30 31 42 41 31 32 43 42 32 33 44 4334 35 46 45 35 36 47 46 36 37 48 47 37 38 49 48 38 39 50 4939 40 51 50 40 41 52 51 41 42 53 52 42 43 54 53 43 44 55 5445 46 57 56 46 47 58 57 47 48 59 58 48 49 60 59 49 50 61 6050 51 62 61 51 52 63 62 52 53 64 63 53 54 65 64 54 55 66 6556 57 68 67 57 58 69 68 58 59 70 69 59 60 71 70 60 61 72 7161 62 73 72 62 63 74 73 63 64 75 74 64 65 76 75 65 66 77 7667 68 79 78 68 69 80 79 69 70 81 80 70 71 82 81 71 72 83 8272 73 84 83 73 74 85 84 74 75 86 85 75 76 87 86 76 77 88 8778 79 90 89 79 80 91 90 80 81 92 91 81 82 93 92 82 83 94 9383 84 95 94 84 85 96 95 85 86 97 96 86 87 98 97 87 88 99 9889 90 101 100 90 91 102 101 91 92 103 102 92 93 104 10393 94 105 104 94 95 106 105 95 96 107 106 96 97 108 10797 98 109 108 98 99 110 109100 101 112 111 101 102 113 112 102 103 114 113 103 104 115 114104 105 116 115 105 106 117 116 106 107 118 117 107 108 119 118108 109 120 119 109 110 121 120122 123 123 124 124 125 125 126 126 127 127 128 128 129 129 130131 132 132 133 133 134 134 126 126 135 135 136 136 137 137 138








LINK COUPBLOQ 1 LECT blox TERMBLOQ 2 LECT bloy TERMBLOQ 12 LECT 126 TERMFLSR STRU LECT stru TERM


!BFLU 0 FSCP 1BFLU 0 FSCP 0ADAP LMAX 4 SCAL 2.0

INIT VITE 1 -80.0 LECT 122 TERM1 -60.0 LECT 123 TERM1 -40.0 LECT 124 TERM1 -20.0 LECT 125 TERM1 20.0 LECT 127 TERM1 40.0 LECT 128 TERM1 60.0 LECT 129 TERM1 80.0 LECT 130 TERM2 80.0 LECT 131 TERM2 60.0 LECT 132 TERM2 40.0 LECT 133 TERM2 20.0 LECT 134 TERM2 -20.0 LECT 135 TERM2 -40.0 LECT 136 TERM2 -60.0 LECT 137 TERM2 -80.0 LECT 138 TERM

ECRI DEPL VITE ACCE FINT FEXT TFRE 10.E-3POIN LECT stru TERMELEM LECT stru TERM





SLER CAM1 1 NFRA 1TRAC OFFS FICH AVI NOCL NFTO 963 FPS 15 KFRE 10 COMP -1 REND

FREQ 1 !FREQ 0 TFRE 1.E-3GOTR LOOP 961 OFFS FICH AVI CONT NOCL RENDGOTRAC OFFS FICH AVI CONT RENDENDPLAY*=================================================================SUITPost-treatmentECHORESU ALIC GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'COUR 1 'dx_130' DEPL COMP 1 NOEU LECT 130 TERMCOUR 2 'vx_130' VITE COMP 1 NOEU LECT 130 TERMTRAC 1 AXES 1.0 'DISPL. [M]'TRAC 2 AXES 1.0 'VELOC. [M/S]'LIST 1 AXES 1.0 'DISPL. [M]'LIST 2 AXES 1.0 'VELOC. [M/S]'*=================================================================FIN

mill04p.epx MILL04PECHORESU ALIC 'mill04.ali' GARD PSCROPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 5.00000E+00 3.53995E+01! Q 1.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00





mill04v.epx MILL04VECHORESU ALIC 'mill04.ali' GARD PSCROPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 5.00000E+00 3.53995E+01! Q 1.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00




mill11.dgibi opti echo 1;opti dime 2 elem qua4;opti titr 'MILL11';opti sauv form 'mill11.msh';opti trac psc ftra 'mill11_mesh.ps';p1 = 0 0;p2 = 10 0;p3 = 10 10;p4 = 0 10;n = 10;c1 = p1 d n p2;c2 = p2 d n p3;c3 = p3 d n p4;c4 = p4 d n p1;flui = dall c1 c2 c3 c4 plan;p122s = 5 1;p123s = 5 2;p124s = 5 3;p125s = 5 4;p126s = 5 5;p127s = 5 6;p128s = 5 7;p129s = 5 8;p130s = 5 9;p131s = 1 5;p132s = 2 5;p133s = 3 5;p134s = 4 5;

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p135s = 6 5;p136s = 7 5;p137s = 8 5;p138s = 9 5;stru1 = p122s d 1 p123s d 1 p124s d 1 p125s d 1 p126s d 1 p127s

d 1 p128s d 1 p129s d 1 p130s;stru2 = p131s d 1 p132s d 1 p133s d 1 p134s d 1 p126s d 1 p135s

d 1 p136s d 1 p137s d 1 p138s;stru = stru1 et stru2;mesh = flui et stru;tass mesh;sauv form mesh;trac qual mesh;fin;

mill11.epx MILL11ECHO!CONV winCAST meshDPLA ALEDIME NALE 1 NBLE 1 TERMGEOM FL24 flui ED01 stru TERMCOMP NGRO 2 'blox' LECT c2 c4 TERM






LINK COUPBLOQ 1 LECT blox TERMBLOQ 2 LECT bloy TERMBLOQ 12 LECT p126s TERMFLSR STRU LECT stru TERM



INIT VITE 1 -80.0 LECT p122s TERM1 -60.0 LECT p123s TERM1 -40.0 LECT p124s TERM1 -20.0 LECT p125s TERM1 20.0 LECT p127s TERM1 40.0 LECT p128s TERM1 60.0 LECT p129s TERM1 80.0 LECT p130s TERM2 80.0 LECT p131s TERM2 60.0 LECT p132s TERM2 40.0 LECT p133s TERM2 20.0 LECT p134s TERM2 -20.0 LECT p135s TERM2 -40.0 LECT p136s TERM2 -60.0 LECT p137s TERM2 -80.0 LECT p138s TERM






SLER CAM1 1 NFRA 1TRAC OFFS FICH AVI NOCL NFTO 962 FPS 15 KFRE 10 COMP -1 RENDFREQ 1 !FREQ 0 TFRE 1.E-3GOTR LOOP 960 OFFS FICH AVI CONT NOCL RENDGOTRAC OFFS FICH AVI CONT RENDENDPLAY*=================================================================SUITPost-treatmentECHORESU ALIC GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'COUR 1 'dx_130' DEPL COMP 1 NOEU LECT p130s TERMCOUR 2 'vx_130' VITE COMP 1 NOEU LECT p130s TERMTRAC 1 AXES 1.0 'DISPL. [M]'TRAC 2 AXES 1.0 'VELOC. [M/S]'LIST 1 AXES 1.0 'DISPL. [M]'LIST 2 AXES 1.0 'VELOC. [M/S]'*=================================================================FIN

mill11p.epx MILL11PECHO

RESU ALIC 'mill11.ali' GARD PSCROPTI PRINSORT VISU NSTO 1*=================================================================PLAYCAME 1 EYE 5.00000E+00 5.00000E+00 3.53995E+01! Q 1.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00









mill12.dgibi opti echo 1;opti dime 2 elem qua4;opti titr 'MILL12';opti sauv form 'mill12.msh';opti trac psc ftra 'mill12_mesh.ps';p1 = 0 0;p2 = 10 0;p3 = 10 10;p4 = 0 10;n = 20;c1 = p1 d n p2;c2 = p2 d n p3;c3 = p3 d n p4;c4 = p4 d n p1;flui = dall c1 c2 c3 c4 plan;p122s = 5 1;p123s = 5 2;p124s = 5 3;p125s = 5 4;p126s = 5 5;p127s = 5 6;p128s = 5 7;p129s = 5 8;p130s = 5 9;p131s = 1 5;p132s = 2 5;p133s = 3 5;p134s = 4 5;p135s = 6 5;p136s = 7 5;p137s = 8 5;p138s = 9 5;stru1 = p122s d 1 p123s d 1 p124s d 1 p125s d 1 p126s d 1 p127s




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INIT VITE 1 -80.0 LECT p122s TERM1 -60.0 LECT p123s TERM1 -40.0 LECT p124s TERM

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1 -20.0 LECT p125s TERM1 20.0 LECT p127s TERM1 40.0 LECT p128s TERM1 60.0 LECT p129s TERM1 80.0 LECT p130s TERM2 80.0 LECT p131s TERM2 60.0 LECT p132s TERM2 40.0 LECT p133s TERM2 20.0 LECT p134s TERM2 -20.0 LECT p135s TERM2 -40.0 LECT p136s TERM2 -60.0 LECT p137s TERM2 -80.0 LECT p138s TERM















SLER CAM1 1 NFRA 1TRAC OFFS FICH AVI NOCL NFTO 962 FPS 15 KFRE 10 COMP -1 RENDFREQ 1GOTR LOOP 960 OFFS FICH AVI CONT NOCL RENDGOTRAC OFFS FICH AVI CONT REND

ENDPLAY*=================================================================FIN
















VIEW 0.00000E+00 0.00000E+00 -1.00000E+00RIGH 1.00000E+00 0.00000E+00 0.00000E+00

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UP 0.00000E+00 1.00000E+00 0.00000E+00FOV 2.48819E+01



mill14compare.epx MILL14COMPAREECHORESU ALIC 'mill14.ali' GARD PSCRSORT GRAPAXTE 1.0 'Time [s]'RCOU 11 'dx_130' FICH 'mill11.pun' RENA 'dx_130_11'RCOU 12 'vx_130' FICH 'mill11.pun' RENA 'vx_130_11'RCOU 21 'dx_130' FICH 'mill12.pun' RENA 'dx_130_12'RCOU 22 'vx_130' FICH 'mill12.pun' RENA 'vx_130_12'RCOU 31 'dx_130' FICH 'mill13.pun' RENA 'dx_130_13'RCOU 32 'vx_130' FICH 'mill13.pun' RENA 'vx_130_13'RCOU 41 'dx_130' FICH 'mill14.pun' RENA 'dx_130_14'RCOU 42 'vx_130' FICH 'mill14.pun' RENA 'vx_130_14'RCOU 121 'dx_130' FICH 'mill02.pun' RENA 'dx_130_02'RCOU 122 'vx_130' FICH 'mill02.pun' RENA 'vx_130_02'RCOU 141 'dx_130' FICH 'mill04.pun' RENA 'dx_130_04'RCOU 142 'vx_130' FICH 'mill04.pun' RENA 'vx_130_04'TRAC 11 21 31 41 AXES 1.0 'DISPL. [M]'COLO NOIR BLEU TURQ VERTTRAC 12 22 32 42 AXES 1.0 'VELOC. [M/S]'COLO NOIR BLEU TURQ VERTTRAC 11 21 31 41 121 AXES 1.0 'DISPL. [M]'COLO NOIR BLEU TURQ VERT ROSETRAC 12 22 32 42 122 AXES 1.0 'VELOC. [M/S]'COLO NOIR BLEU TURQ VERT ROSETRAC 41 141 AXES 1.0 'DISPL. [M]'COLO VERT ROUGTRAC 42 142 AXES 1.0 'VELOC. [M/S]'COLO VERT ROUG*=================================================================FIN








SCEN GEOM NAVI FREEFACE HFRO

LINE HEOU SFREVECT SCCO FIEL VITE SCAL USER PROG 10 PAS 10 140 TERMTEXT VSCACOLO PAPE


Page 85

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List of input files

fsia06.epx . . . . . . . . . . . . . . . . . . . . . . . 62fsia06p.epx . . . . . . . . . . . . . . . . . . . . . . 62fsia06v.epx . . . . . . . . . . . . . . . . . . . . . . 62fsia09.epx . . . . . . . . . . . . . . . . . . . . . . . 62fsia09p.epx . . . . . . . . . . . . . . . . . . . . . . 63fsia09v.epx . . . . . . . . . . . . . . . . . . . . . . 63fsia10.epx . . . . . . . . . . . . . . . . . . . . . . . 63fsia10p.epx . . . . . . . . . . . . . . . . . . . . . . 64fsia10v.epx . . . . . . . . . . . . . . . . . . . . . . 64fsia11.dgibi . . . . . . . . . . . . . . . . . . . . . . 64fsia11.epx . . . . . . . . . . . . . . . . . . . . . . . 64fsia11p.epx . . . . . . . . . . . . . . . . . . . . . . 64fsia11v.epx . . . . . . . . . . . . . . . . . . . . . . 65fsia12.dgibi . . . . . . . . . . . . . . . . . . . . . . 65fsia12.epx . . . . . . . . . . . . . . . . . . . . . . . 65fsia12p.epx . . . . . . . . . . . . . . . . . . . . . . 65fsia12v.epx . . . . . . . . . . . . . . . . . . . . . . 65fsia13.dgibi . . . . . . . . . . . . . . . . . . . . . . 65fsia13.epx . . . . . . . . . . . . . . . . . . . . . . . 66fsia13p.epx . . . . . . . . . . . . . . . . . . . . . . 66fsia13v.epx . . . . . . . . . . . . . . . . . . . . . . 66fsia14.dgibi . . . . . . . . . . . . . . . . . . . . . . 66fsia14.epx . . . . . . . . . . . . . . . . . . . . . . . 66fsia14compare.epx . . . . . . . . . . . . . . . . . . 67fsia14p.epx . . . . . . . . . . . . . . . . . . . . . . 67fsia14v.epx . . . . . . . . . . . . . . . . . . . . . . 67fsia16.epx . . . . . . . . . . . . . . . . . . . . . . . 67fsia16p.epx . . . . . . . . . . . . . . . . . . . . . . 68fsia16v.epx . . . . . . . . . . . . . . . . . . . . . . 68fsia19.epx . . . . . . . . . . . . . . . . . . . . . . . 68fsia19p.epx . . . . . . . . . . . . . . . . . . . . . . 68fsia19v.epx . . . . . . . . . . . . . . . . . . . . . . 69fsia20.epx . . . . . . . . . . . . . . . . . . . . . . . 69fsia20p.epx . . . . . . . . . . . . . . . . . . . . . . 69fsia20v.epx . . . . . . . . . . . . . . . . . . . . . . 69fsia21.dgibi . . . . . . . . . . . . . . . . . . . . . . 70fsia21.epx . . . . . . . . . . . . . . . . . . . . . . . 70fsia21p.epx . . . . . . . . . . . . . . . . . . . . . . 70fsia21v.epx . . . . . . . . . . . . . . . . . . . . . . 70fsia22.dgibi . . . . . . . . . . . . . . . . . . . . . . 70fsia22.epx . . . . . . . . . . . . . . . . . . . . . . . 70fsia22p.epx . . . . . . . . . . . . . . . . . . . . . . 71fsia22v.epx . . . . . . . . . . . . . . . . . . . . . . 71fsia23.dgibi . . . . . . . . . . . . . . . . . . . . . . 71fsia23.epx . . . . . . . . . . . . . . . . . . . . . . . 71fsia23p.epx . . . . . . . . . . . . . . . . . . . . . . 71fsia23v.epx . . . . . . . . . . . . . . . . . . . . . . 72fsia24.dgibi . . . . . . . . . . . . . . . . . . . . . . 72fsia24.epx . . . . . . . . . . . . . . . . . . . . . . . 72fsia24compare.epx . . . . . . . . . . . . . . . . . . 72fsia24p.epx . . . . . . . . . . . . . . . . . . . . . . 72fsia24v.epx . . . . . . . . . . . . . . . . . . . . . . 73fsia26.dgibi . . . . . . . . . . . . . . . . . . . . . . 73fsia26.epx . . . . . . . . . . . . . . . . . . . . . . . 73fsia26a.epx . . . . . . . . . . . . . . . . . . . . . . 73fsia26b.epx . . . . . . . . . . . . . . . . . . . . . . 73fsia26p.epx . . . . . . . . . . . . . . . . . . . . . . 73fsia26v.epx . . . . . . . . . . . . . . . . . . . . . . 73

fsia31.dgibi . . . . . . . . . . . . . . . . . . . . . . 74fsia31.epx . . . . . . . . . . . . . . . . . . . . . . . 74fsia31p.epx . . . . . . . . . . . . . . . . . . . . . . 74fsia31v.epx . . . . . . . . . . . . . . . . . . . . . . 74fsia32.dgibi . . . . . . . . . . . . . . . . . . . . . . 75fsia32.epx . . . . . . . . . . . . . . . . . . . . . . . 75fsia32p.epx . . . . . . . . . . . . . . . . . . . . . . 75fsia32v.epx . . . . . . . . . . . . . . . . . . . . . . 75fsia33.dgibi . . . . . . . . . . . . . . . . . . . . . . 75fsia33.epx . . . . . . . . . . . . . . . . . . . . . . . 76fsia33a.epx . . . . . . . . . . . . . . . . . . . . . . 76fsia33b.epx . . . . . . . . . . . . . . . . . . . . . . 76fsia33compare.epx . . . . . . . . . . . . . . . . . . 76fsia33p.epx . . . . . . . . . . . . . . . . . . . . . . 76fsia33v.epx . . . . . . . . . . . . . . . . . . . . . . 76fsia36.dgibi . . . . . . . . . . . . . . . . . . . . . . 77fsia36.epx . . . . . . . . . . . . . . . . . . . . . . . 77fsia36a.epx . . . . . . . . . . . . . . . . . . . . . . 77fsia36b.epx . . . . . . . . . . . . . . . . . . . . . . 77fsia36p.epx . . . . . . . . . . . . . . . . . . . . . . 77fsia36v.epx . . . . . . . . . . . . . . . . . . . . . . 77fsia41.dgibi . . . . . . . . . . . . . . . . . . . . . . 78fsia41.epx . . . . . . . . . . . . . . . . . . . . . . . 78fsia41a.epx . . . . . . . . . . . . . . . . . . . . . . 78fsia41b.epx . . . . . . . . . . . . . . . . . . . . . . 78fsia41p.epx . . . . . . . . . . . . . . . . . . . . . . 78fsia41v.epx . . . . . . . . . . . . . . . . . . . . . . 78fsia42.dgibi . . . . . . . . . . . . . . . . . . . . . . 79fsia42.epx . . . . . . . . . . . . . . . . . . . . . . . 79fsia42a.epx . . . . . . . . . . . . . . . . . . . . . . 79fsia42b.epx . . . . . . . . . . . . . . . . . . . . . . 79fsia42p.epx . . . . . . . . . . . . . . . . . . . . . . 79fsia42v.epx . . . . . . . . . . . . . . . . . . . . . . 79fsia43.dgibi . . . . . . . . . . . . . . . . . . . . . . 80fsia43.epx . . . . . . . . . . . . . . . . . . . . . . . 80fsia43a.epx . . . . . . . . . . . . . . . . . . . . . . 80fsia43b.epx . . . . . . . . . . . . . . . . . . . . . . 80fsia43p.epx . . . . . . . . . . . . . . . . . . . . . . 80fsia43v.epx . . . . . . . . . . . . . . . . . . . . . . 80mill04.epx . . . . . . . . . . . . . . . . . . . . . . 81mill04p.epx . . . . . . . . . . . . . . . . . . . . . . 81mill04v.epx . . . . . . . . . . . . . . . . . . . . . . 81mill11.dgibi . . . . . . . . . . . . . . . . . . . . . . 81mill11.epx . . . . . . . . . . . . . . . . . . . . . . 82mill11p.epx . . . . . . . . . . . . . . . . . . . . . . 82mill11v.epx . . . . . . . . . . . . . . . . . . . . . . 82mill12.dgibi . . . . . . . . . . . . . . . . . . . . . . 82mill12.epx . . . . . . . . . . . . . . . . . . . . . . 82mill12p.epx . . . . . . . . . . . . . . . . . . . . . . 83mill12v.epx . . . . . . . . . . . . . . . . . . . . . . 83mill13.dgibi . . . . . . . . . . . . . . . . . . . . . . 83mill13.epx . . . . . . . . . . . . . . . . . . . . . . 83mill13p.epx . . . . . . . . . . . . . . . . . . . . . . 84mill13v.epx . . . . . . . . . . . . . . . . . . . . . . 84mill14.dgibi . . . . . . . . . . . . . . . . . . . . . . 84mill14.epx . . . . . . . . . . . . . . . . . . . . . . 84mill14compare.epx . . . . . . . . . . . . . . . . . . 85mill14p.epx . . . . . . . . . . . . . . . . . . . . . . 85mill14v.epx . . . . . . . . . . . . . . . . . . . . . . 85

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European Commission

EUR 26617 – Joint Research Centre – Institute for the Protection and Security of the Citizen

Title: Combination of Mesh Adaptivity with Fluid-Structure Interaction in EUROPLEXUS

Author(s): Folco Casadei, Georgios Valsamos, Martin Larcher, Alberto Beccantini

Luxembourg: Publications Office of the European Union

2014 – 91 pp. – 21.0 x 29.7 cm

EUR – Scientific and Technical Research series – ISSN 1831-9424

JRC89728

ISBN 978-92-79-37851-5

DOI 10.2788/61547

Abstract

The present work concerns a new aspect of mesh adaptivity, i.e. the automatic refinement of the fluid mesh near a structure, in

order to enhance the treatment of Fluid-Structure Interaction (FSI). This technique is particularly useful in conjunction with FSI

algorithms of the embedded or immersed type, such as the FLSR or FLSW algorithms available in the EUROPLEXUS code for fast

transient dynamics.

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ISBN 978-92-79-37851-5

DOI 10.2788/61547

Documents

Combination of Mesh Adaptivity with Fluid-Structure ...publications.jrc.ec.europa.eu/repository/bitstream/JRC89728/lbna26617enn.pdfMartin Larcher Alberto Beccantini Combination of